Stats sourced from the code, at the discretion of the developers.

You can switch ministers at any time from the Politics screen by clicking the button that lights up when hovered over next to the current Minister's portrait, at an incurred cost of -5 party unity, -0.1 money, and +1.0 westalgia. A new leader, on the other hand, can only take power in certain events.
The listed effects of course trigger at the end of each week, meaning on the 7th, 14th, 21st and 28th day of each month, unless listed otherwise.

Keep in mind that there are many other potential factors like state doctrines, sovereignty, patriotism and trade balance that can impact various stats, so it's unlikely that your weekly changes will simply equal the sum of your leader and ministers.

Sovmin:

Sharq:
-Party Support -0.5
-Westalgia -0.3

Keshtmand:
-Research goes 1 science building faster
-Standard of Living +0.2

Wakil:
-Party Support +0.3
-Westalgia +0.3
-Agents +0.2


Ideology:

Chamkani:
-Party Support +0.6
-Westalgia +0.2

Watanjar:
-Agents +0.2
-Westalgia +0.5
-Party Support +0.3

Qadir:
-Party Support -0.5
-Westalgia -0.3 if more than 40.0
-Support of the People +0.4 if less than 40.0


Leaders:

Najbullah:
-Party Support +0.3
-Support of the People +0.3
-Westalgia -0.2

Tanay:
-Agents +0.2
-Party Support -0.4
-Westalgia -0.4
-Diplomatic Reputation +0.2
-USSR Approval -0.4

Dustum:
-Support of the People +0.1
-USSR Approval +0.4
-Diplomatic Reputation -0.2 if over 40.0

Sovmin:

Carcani:
-Party Support +0.4

Murra:
-Support of the People -0.4
-Westalgia -0.2
-USSR Approval -0.4
-Agents +0.2

Berisha:
-Support of the People +0.3
-Westalgia +0.2
-NATO Threat -0.1
-Money +0.2
-Standard of Living -0.2
-Party Support -0.4 and Money -0.4 if the State System isn't Social Democracy or Liberalism, or if Hoxha is the Leader


Ideology:

Cuko:
-Support of the People -0.2
-Westalgia -0.2
-Party Support +0.2
-USSR Approval -0.4
-Diplomatic Reputation +0.1 if the year is 1990 or later

Bufi:
-Research goes 1 science building faster
-Party Support -0.4
-Westalgia +0.2
-Standard of Living +0.2

Pashko:
-Support of the People +0.2
-Patriotism +0.1
-Party Support -0.4 and Money -0.4 if the State System isn't Social Democracy or Liberalism, or if Hoxha is the Leader


Leaders:

Alia:
-Support of the People +0.5
-Westalgia -0.8
-USSR Approval +0.1
-Party Support +0.1
-Sovereignty -0.1 if over 50.0
-Patriotism -0.1 if over 50.0

Hoxha:
-Westalgia -1.1
-Party Support +0.4
-USSR Approval -0.4
-Sovereignty +0.2
-Patriotism +0.2
-NATO Threat +0.1
-Standard of Living -0.1
-Diplomatic Reputation +0.1

Nano:
-Westalgia -0.9
-USSR Approval +0.1
-Party Support -0.1
-Sovereignty -0.1
-Patriotism -0.2
-Standard of Living -0.1

Sovmin:

Atanasov:
-Party Support +0.5
-Westalgia +0.1
-Money -0.1

Lukanov:
-Party Support -0.2
-Support of the People +0.5
-Westalgia +0.5
-Agents -0.2
-Money +0.3
-USSR Approval +0.2
-NATO Threat -0.1

Stoyanov:
-USSR Approval -0.4
-Support of the People -0.5
-Westalgia -0.5
-Standard of Living -0.1
-Diplomatic Reputation +0.1 if less than 80.0 and before 1992
-NATO Threat +0.1
-Agents +0.2


Ideology:

Balev:
-Party Support +0.3 if Ruler is Solakov, otherwise +0.5
-Westalgia +0.1
-Money -0.1
-Sovereignty +0.1 if less than 50.0
-Agents -0.1

Filipov:
-Party Line -0.2 if over 60.0, otherwise +0.1
-Standard of Living +0.1 if under 65.0
-USSR Approval +0.1
-Westalgia +0.3
-Money +0.1

Popov:
-Party Support -0.5 if the State System isn't Authoritarianism or Liberalism, otherwise +0.5
-Support of the People +0.1
-Westalgia +0.2
-Agents +0.2
-NATO Threat +0.2
-Patriotism +0.1


Leaders:

Zhivkov:
-Party Line +0.2 if under 85.0 when State System is Authoritarian, Developed Socialism or Thaw
-Party Support - (current Party Support / 100)
-USSR Approval -0.2
-Westalgia -0.7 if over 30.0
-Support of the People +0.7 if under 90.0
-Diplomatic Reputation +0.1 if under 90.0
-Patriotism -0.1 if over 60.0, +0.1 if under 50.0
-Agents +0.2
-Money -0.2

Mladenov:
-Party Line -0.1 if over 75.0, otherwise +0.1
-USSR Approval +0.5
-Westalgia +0.4
-Party Support -0.5
-Support of the People +0.5
-Patriotism -0.1 if over 50.0

Solakov:
-Party Line +0.2 if under 90.0
-Agents +0.1
-USSR Approval -0.4
-Westalgia -0.2
-Support of the People -0.6
-NATO Threat +0.1
-Patriotism +0.1 if under 70.0

Lilov:
-USSR Approval +0.6
-Support of the People +0.5
-Party Support -0.5
-Westalgia +1.0
-NATO Threat -0.1
-Patriotism -0.1
-Diplomatic Reputation -0.1 if under 60.0 and before 1992
-Agents -0.1
-Money +0.2

Sovmin:

Borrego:
-Money +0.4 if the Economic System is Late Planned or Automation, otherwise +0.2
-Party Support +0.1
-Support of the People -0.3
-Westalgia +0.2

Ramon
-Money -0.2
-Party Support -0.3
-Standard of Living +0.4
-Support of the People +0.3
-Westalgia +0.2

Hart:
-USSR Approval +0.2
-Westalgia +0.4
-Support of the People +0.6
-Party Support -0.3


Ideology:

Frias:
-Agents +0.2
-NATO Threat +0.2
-Westalgia -0.2
-Support of the People -0.5

Barra:
-Socialist Camp Stability will decrease by 0.2 less at the end of each month if Barra holds office on the last day of it
-Party Support +0.2
-USSR Approval +0.2
-Westalgia -0.1
-NATO Threat +0.3

Valdes:
-Research goes 1 science building faster
-Party Support -0.6
-Money +0.2 if the Economic System is Late Planned or Automated and the Special Period is active


Leaders:

Fidel:
-Support of the People +0.2
-Party Support +0.4
-Westalgia +0.3
-Agents +0.1

Raul:
-Support of the People +0.4
-Support of the People +0.3 if (current Support of the People) - (the number of turns it has been since Raul took office) > 0 damn, dude
oh wait, there's more
-Support of the People + (50.0 - (current Support of the People) / 10.0 x 3)
-Westalgia -0.2
-Party Support +0.7
-Westalgia +0.2
-NATO Threat +0.1

T. Ochoa:
-Support of the People +0.2
-Party Support -0.3
-Westalgia +0.2
-USSR Approval +0.4

Sovmin:

Jakes:
-USSR Approval +0.1
-Money +0.2
-Standard of Living -0.2
-Party Support -0.1

Urbanek:
-USSR Approval +0.2
-Westalgia +0.3
-Support of the People +0.2

Cernik:
-USSR Approval +0.3
-NATO Threat -0.2
-Support of the People +0.2
-Westalgia +0.5


Ideology:

Calfa:
-USSR Approval +0.2
-NATO Threat -0.2
-Westalgia +0.2
-Party Support -0.2

Vaclavik:
-USSR Approval -0.2
-NATO Threat +0.1
-Westalgia -0.4
-Support of the People -0.2
-Agents +0.2

Miller:
-USSR Approval +0.1
-NATO Threat -0.2
-Westalgia +0.4
-Support of the People +0.2
-Party Support -0.6 if State System isn't Social Democracy or Liberalism


Leaders:

Husak:
-Party Support +0.8
-Westalgia +0.2
-Standard of Living +0.4

Adamec:
-USSR Approval +0.1
-Party Support +0.2
-Support of the People +0.1
-Westalgia +0.2

Strougal:
-USSR Approval +0.3
-Party Support -0.2
-Support of the People +0.2
-Westalgia +0.3

Havel:
-NATO Threat -0.2
-Sovereignty -0.2
-Agents -0.2
-If State System isn't Social Democracy or Liberalism: Money -0.2; +1 liberalization to Parties doctrine type if not Free, if Free Parties +1 liberalization to Freedom doctrine type if not Liberal Freedoms, if Free Parties and Liberal Freedoms +1 liberalization to Type of Economy doctrine type if not Regulated Market

Sovmin:

Stoph:
-Party Line +0.2 if the Leader is Krenz or Gysi
-Westalgia +0.4
-Party Support +0.4
-USSR Approval -0.4
-Sovereignty +0.2 if less than 70.0
-Money +0.2
-Standard of Living -0.1
-Agents +0.1
-Support of the People -0.4

Sindermann:
-Party Line -0.2 if above 60.0, otherwise +0.1
-Standard of Living +0.1 if less than 65.0
-USSR Approval -0.2
-Westalgia +0.4
-Money +0.1

Modrow:
-Party Line -0.4 if above 60.0, otherwise -0.2
-USSR Approval +0.4
-Support of the People +0.4
-Westalgia +1.2
-NATO Threat -0.1
-Patriotism -0.1
-Diplomatic Reputation -0.1 if over or equal to 40.0 and if it's not after 1991 (so until the end of the game proper)


Ideology:

Hager:
-Party Line +0.2 if the Leader is Krenz or Gysi
-Westalgia +0.4
-Party Support +0.8
-USSR Approval -0.2
-Sovereignty +0.4 if less than 70.0
-Standard of Living -0.1
-Agents +0.1
-Patriotism +0.1 if less than 65.0
-Support of the People -0.4

Kleiber:
-Standard of Living +0.1 if less than 70.0, if less than 60.0 and the third automation technology hasn't been researched, or if less than 50.0 and the second automation tech hasn't been researched
-USSR Approval -0.2
-Party Support -1.2
-Money +0.1
-Westalgia -0.2
-It's necessary to have him appointed to get the Classified Achievement.

Schabowski:
-Party Line -0.2
-USSR Approval +0.4
-Support of the People -0.2
-Westalgia +0.2


Leaders:

Hochnecker:
-When the State System is Authoritarianism, Developed Socialism or Thaw: Party Line +0.2 if under 90.0, otherwise -0.1
-Westalgia +0.1
-Party Support +0.1
-USSR Approval -0.2
-Diplomatic Reputation +0.1 if under 90.0
-NATO Threat +0.1
-Patriotism -0.1 if over 50.0

Mielke:
-Party Line +0.2 if under 90.0, otherwise +0.1
-Agents +0.1
-USSR Approval -1.2
-Party Support -0.8
-Westalgia -0.8
-Support of the People -0.4
-Patriotism +0.1 if less than 65.0

Krenz:
-Party Line -0.2 if over 60.0, otherwise +0.1
-USSR Approval +0.4
-Support of the People +0.2
-Westalgia +0.4
-Party Support -1.0
-Patriotism -0.1 if over 30.0

Gysi:
-Party Line -0.4 if over 60.0, otherwise -0.2
-USSR Approval +0.6
-Support of the People +0.6
-Party Support +0.6
-Westalgia +1.2
-NATO Threat -0.1
-Patriotism -0.1
-Diplomatic Reputation -0.1 if over 40.0 and before 1991

Sovmin:

Karpati:
-Support of the People +0.2
-Agents -0.1

Hegedus:
-Research goes 1 science building faster
-Support of the People +0.2
-Westalgia +0.2 for every year past 1988

F(o)ck:
-USSR Approval +0.2
-Money +0.2
-Westalgia +0.3
-Sovereignty -0.1


Ideology:

Horn:
-USSR Approval +0.3
-NATO Threat -0.1
-Westalgia +0.3

Pozsgay:
-Patriotism +0.1 if under 80.0
-USSR Approval -0.1
-Support of the People +0.2
-Westalgia +0.2
-Sovereignty +0.1 if under 50.0

Lazar:
-USSR Approval -0.2
-Money +0.2
-Standard of Living +0.1


Leaders:

Grosz:
-USSR Approval +0.2
-Support of the People -0.2
-Westalgia +0.2
-Party Support -0.1
-Part Support - [(current party support - 40.0) / 10.0] if equal to or over 50.0
-Part Support - [(current party support - 40.0) / 5.0] if equal to or over 70.0
-Part Support - [(current party support - 40.0) / 2.5] if equal to or over 80.0
(All 3 of the above apply if party support >= 80.0)

Nemeth:
-USSR Approval +0.3
-Sovereignty -0.1
-Patriotism -0.1
-Westalgia +0.3

Borbely:
-USSR Approval -0.2
-Agents +0.2
-Support of the People +0.1
-Party Support +0.1
-NATO Threat +0.1
-Patriotism +0.1 if over 50.0, if 50 or less but over 30.0 then -0.2 interesting

Krausz:
-Party Support +0.1
-USSR Approval -0.1
-Support of the People +0.1
-Westalgia -0.1
-Patriotism -0.2 if over 50.0, if 50 or less but over 30.0 then -0.1

Sovmin:

Jang Song-Thaek:
-Research goes 1 science building faster
-Standard of Living +0.1
-Westalgia +0.3

Yong Hyung-Mook:
-NATO Threat -0.5
-Party Support -0.3
-USSR Approval +0.1
-Sovereignty -0.1
-Diplomatic Reputation -0.1 if above 70.0

Pak Pong-Ju:
-Party Support -0.5
-Money +0.2
-Westalgia +0.3


Ideology:

Kim Khnam:
-Westalgia -0.5
-Support of the People +0.4
-NATO Threat +0.1
-USSR Approval -0.1

Choe Kwang:
-NATO Threat +0.3
-Agents +0.2
-Diplomatic Reputation +0.2
-Westalgia -0.3

Kim Yong-Ju:
-Party Support +0.8
-Support of the People -0.1
-Westalgia +0.6


Leaders:

Kim Il-Sung:
-Support of the People +0.5
-Party Support +0.5
-Patriotism +0.1
-Sovereignty +0.1
-Support of the People +0.4 after 1990

O Jin-U:
-Agents +0.2
-Support of the People -0.3
-Party Support -0.4
-Diplomatic Reputation +0.2
-Patriotism +0.1 if under 70.0
-Sovereignty +0.1

Kim Jong-Il:
-Support of the People +0.5
-Party Support +0.3
-Patriotism +0.1 if under 70.0
-Sovereignty +0.1

Kim Yong-Chun:
-Support of the People +0.5
-Westalgia +0.3
-Party Support -0.4
-Sovereignty -0.1 if above 30.0

Sovmin:

Messner:
-Party Support +0.2
-Support of the People -0.3
-Westalgia +0.3
-Standard of Living -0.3
-Money +0.3

Rakowski:
-Party Support -0.1
-Support of the People +0.4
-Westalgia +0.4
-Agents -0.1
-Money +0.2
-USSR Approval +0.4
-NATO Threat -0.1
-Sovereignty -0.1

Kiszczack:
-Party Support +0.5
-USSR Approval +0.2
-Support of the People -0.3
-Westalgia +0.3


Ideology:

Ciosek:
-Party Support +0.3
-Westalgia -0.2
-Support of the People +0.2
-Money -0.2
-Sovereignty +0.1 if below 70.0
-Standard of Living -0.1
-Agents +0.1

Baryla:
-Party Line +0.1
-Support of the People -0.4
-Westalgia +0.4
-Party Support +0.8
-USSR Approval -0.2
-Sovereignty +0.3 if below 70.0
-Standard of Living -0.1
-Agents +0.2
-Patriotism +0.1 if below 65.0

Hupalowski:
-Party Support +0.5
-Westalgia +0.1
-Money -0.1
-Sovereignty +0.1 if below 50.0
-Money +0.2 and Agents +0.1 if the Economic System is State Capitalism or Regulated Market


Leaders:

Jaruzelski:
-Party Line -0.1
-Party Support +0.6
-USSR Approval +0.3
-Support of the People -0.2
-Westalgia +0.2
-Agents +0.1
-Standard of Living -0.2

Siwak:
-Party Line +0.1
-Sovereignty +0.1
-Patriotism +0.2
-Party Support +0.2
-USSR Approval -0.5
-Support of the People -0.8
-Westalgia +0.5
-Standard of Living -0.3
-Diplomatic Reputation +0.2
-Agents +0.1
-NATO Threat +0.1

Kwasniewski:
-Party Line -0.1
-Sovereignty -0.1
-Patriotism -0.1
-Party Support +0.2
-USSR Approval -0.5
-Support of the People +0.2
If joining the EEC:
-Westalgia +0.2
-Agents -0.2
-NATO Threat -0.1
If not joining the EEC:
-Westalgia +0.8
-Standard of Living +0.1
-Diplomatic Reputation -0.1
-Agents -0.1
-NATO Threat -0.2

Sovmin:

Dascalescu:
-Party Support +0.5
-Westalgia -0.1
-Support of the People +0.1 until 1990 if Ceausescu is the Leader, otherwise -0.1
-Money -0.1
-Sovereignty +0.1 if less than 70.0

Dinca:
-Party Support -0.2
-Support of the People -0.5
-Westalgia -0.5
-Agents +0.2
-Money -0.1
-USSR Approval -0.2

Andrei:
-Sovereignty +0.2
-USSR Approval -0.4
-Support of the People +0.2
-Westalgia +0.2
-Standard of Living +0.1
-Diplomatic Reputation -0.1 if above 80.0 and before 1992
-NATO Threat +0.1
-Patriotism -0.1 if more than 65.0
-Money +0.2


Ideology:

Bobu:
-Party Support +0.3
-Westalgia +0.1
-Support of the People +0.3 if the year is 1989 and Ceausescu is the Leader, otherwise +0.1
-Money -0.1
-Sovereignty +0.1 if less than 70.0
-Standard of Living -0.1
-Agents +0.1

Militaru:
Party Support -1.0 if the state system is Authoritarianism, the country is integrating into the EEC, or the country has left the CMEA or WPO, otherwise +0.2
-USSR Approval +1.0
-Support of the People +0.2
-Westalgia +0.5
-Agents -0.1
-NATO Threat -0.2
-Standard of Living +0.1

Pirvulescu:
-Party Support -1.0 if the state system is Authoritarianism or Social Democracy or Liberalism, Party Line is less than 80.0, the Economic System is Regulated Market, or the country is integrating into the EEC, otherwise +0.2
-Support of the People +0.1
-Westalgia -0.2
-Agents +0.2
-NATO Threat +0.2


Leaders:

Ceausescu:
-If political System isn't Social Democracy or Liberalism: Party Line +0.2 if between 90.0 and 100.0, +0.1 if under 90.0
-Westalgia +0.2
-Party Support +0.5
-USSR Approval -0.2
-Diplomatic Reputation +0.1 if under 90.0
-NATO Threat +0.1
-Patriotism +0.1 if under 70.0, -0.1 if over 70.0
-Agents +0.1
-Support of the People +0.2

Apostol:
-Party Line +0.2 if under 90.0
-Agents +0.1
-USSR Approval -0.2
-Westalgia -0.2
-Support of the People -0.3
-Patriotism +0.1 if under 60.0

Verdet:
-Party Line -0.1 if over 80.0, otherwise -0.1
-USSR Approval +0.2
-Westalgia +0.4
-Party Support -0.5
-Patriotism -0.1 if over 50.0
-Money +0.2

Iliescu:
-USSR Approval +0.6
-Support of the People +0.5
-Party Support -1.0
-Westalgia +1.0
-NATO Threat -0.1
-Patriotism -0.1
-Diplomatic Reputation -0.1 if above 60.0 and before 1992
-Agents +0.1

Sovmin:

Kadijević, while Yugoslavia:
-Party Support +0.3
-Westalgia +0.2
-Agents +0.9
-Party Line +0.2
-Patriotism +0.3

Trifunović, while Yugoslavia:
-Westalgia -0.5
-Popular Support -0.1
-Agents +0.5
-Diplomatic Reputation +0.5
-Money +0.5
-Party Line +0.1
-Patriotism -0.1

Manolić, while Yugoslavia:
-Party Support -0.4
-Westalgia +0.2
-NATO Threat -0.5
-Money +0.5
-Patriotism -0.1
-Party Line -0.2


Ideology:

Lončar, while Yugoslavia:
-Party Support +0.3
-NATO Threat -0.5
-Patriotism +0.1
-Party Line -0.1

Abdić, while Yugoslavia:
-Party Support: -0.2
-Living Standards: -0.2
-Money +0.5
-Party Line +0.1

Marković, while Yugoslavia:
-Popular Support +0.2
-Westalgia +0.8
-Living Standards +0.2
-Money +0.2
-NATO Threat -0.5
-Exports -0.1
-Party Line -0.3


Leaders:
Work in Progress

The rest of the leaders, different country variants for each Yugoslav variants.