No

No

Yes

Maybe

No.

The game has always been easy to catch up on. In fact, there really isn't anything important that you really need to catch up on at all.

Sure, there are a few new weapons and changes to a few old weapons, but everything is still relatively the same in-game. If you are worried about being rusty, TF2 isn't a hard game to get "good" at or even remaster in the first place.

Overall, I absolutely reccomend you do go back into TF2, as it is still an extremely fun game and actually has several new custom gamemodes (some unofficial) like Zombie Fortress that have become extremely fun on the right servers, just incase you do in fact get bored of the normal ways of play.

Short Answer: Yes

Sensitivity depends on class in my opinion. In fact, you might actually be better off having a separate sensitivity for playing sniper while scoped and another sensitivity for pretty much everything else, although adding more is sometimes useful for certain people, specificially when hitscan weapons are concerned. I honestly think you need to test out different sensitivities and find the one that feels the most comfortable to you, not what you happen to immediately perform best at. You can always change them later and there really isn't a set level for everyone, so I wouldn't worry about min-maxing it right away.

No