Just a clarification on the rules. You can't place all pieces "anywhere on the board." Pawns can't be placed in the first or last rows so no illegal placements and no instant promotion.
It's been at least a couple of decades since I've played bug house, so my memories are pretty hazy.
Yes you can. Very often the game ends when a player uses a new piece to checkmate.
More details here http://en.wikipedia.org/wiki/Bughouse_chess