1. Are you trying to put them into sectors that can be used as spawn points? EU groups can spawn at Foch, Japanese on the islands, Korea in Busan and so on
2 and 4 - rest units. Cohesion and initiative blocks them from participating in offensive battles.
5. You can do so only by zooming in the unit, and out of it. I see no reason to do so anyway

1. Some units can only be deployed in specific sectors, for example, kaijo jietai units can only be deployed in naval sector hotel, Ark Royal and Foch naval groups only in naval sector Echo and paratroopers only in Fukuoka. If you lose the specific sector, you cannot deploy the unit.
2. Unit needs at least 1 initiative point to participate in battle
3. Units can only move through sectors that are connected by an arrow sign
4. Naval units don't join amphibious battles. Only marine and naval aviation units will participate in amphibious ground battles. Your marine infantry landing unit contains sea unit for you to capture sea zones.
5. Just select and zoom into the unit you want, then the camera will automatically track on the unit, even when you zoom out.