Officially most of it depends on the team competition, it will have regulations. But I think these questions will have pretty much the same answers everywhere.
- Yes, you're sitting right next to them, and you can walk around as usual, so you can see their boards.
Usually teams have a team leader also, whose role is to advise you about offering or accepting a draw (but not in a way that gives you information about his opinion of your own position! If you ask him "Can I offer a draw?", he must answer yes or no immediately; he can't walk up to your board, think for a while, then say no. It would be obvious then that he thought you had the better position, which is a big no-no). He can otherwise watch all games all the time though.
You can leave if you want. The team leader has to sign the result form at the end, but the players are done when their game is over. Most of the time you'll be eager to know the end result and stay, though.
Re-entering the hall really depends on the regulations. You'll be a spectator. In most amateur leagues, spectators can just stand next to the boards if they wish, so so can you.
Officially you can not speak to anybody during any chess game, including team matches. Practice is slightly less rigorous. If you discuss the ongoing chess games, you're definitely over the line.
No, of course you can't analyze a game right next to ongoing games, that's clearly distracting for the players. Usually there will be a separate room where games can be analyzed.