"A piece which is next to an opponent's stronger piece is considered to be frozen and cannot move on its own"
Would the lesser piece be required to end its move at this point?
Yes. as soon as the lesser piece is next to an opponent's stronger piece, it can't move (unless adjacent to one of it's own pieces)
"A player may push or pull the opponent's rabbit into the goal row it is trying to reach. If at the end of the turn the rabbit remains there, the player loses. However if the opponent's rabbit is moved back out of the goal row before the end of the turn, the player does not lose"
So, if a rabbit is moved involuntarily to the spot where it would have won, it can lose?
This means if player 1 moves player 2's rabbit to players 1 goal row and leaves it there, player 1 loses. If player 1 moves it before the end of his turn, player 1 does not lose.