See the related link below.
Yes both TMs and HMs have unlimited uses in Pokemon Black and White.
no
You do not get any HMs in Castelia City.
There are 95 TMs and 6 HMs in the game. That's the total of 101 HMs and TMs in the game.
there is none
In the top of the battle tower
cheat
the pokemart part of a Pokemon center you can sell HMS or tms you don't need TMs cannot be sold in Black and White.
You have to beat all the gym leaders..
in bushes,with people, in caves, and hidden
nothing will
I think it is piplup because it can learn all the HMs (not fly of course) when it evolves.