It probably is playable on Vista but with some inevitable issues. Also, you can reroll skills ever since 1.13 i think. Yes you can play on battle.net its still up (multiplayer). And you can use a resolution mod if you play on single player.
I can't see them shutting down the servers soon. Especially since every time I ever went back and played it seems during the new ladder season tons of people are playing. I'd say there is a couple more ladder seasons at least before they shut down the servers (if they do). But Diablo 2 is getting older and older.
I am thinking about starting up a lightning sorc or something if I get bored of D3 anytime soon.