1. There are 14 (technically 15 if you know someone with Black 2)
2. That would be a bit annoying to list, so consult this list.
3. Yes there is, but AR codes can't be discussed on these forums. Your search engine of choice is your best friend.
4. That's really up to you, I myself did not use my Master Ball. And no, you cannot catch Mew or Mewtwo in-game. You have to trade with others or transfer them from an older Gen game.
5. Pokemon Mystery Dungeon isn't really for everyone. I enjoy the game somewhat, but if you don't enjoy just walking around and pretty much clicking "A" all the time, then give this one a pass.
6. I suggest getting at least White and playing that first, since White 2 is the sequel. It isn't really all that necessary to get all four games unless you really want to.
7. You can catch Heatran in Reversal Mountain after you obtain the National Pokedex (Beat the E4 and the Champion).