Are there positions where a zugzwang helps the zugzwang'ed player? For instance, white forces black to make a move that gives black an advantage. Is that possible?
Like Brian Towers wrote, a zugzwang by definition can't be helpful to the recipient, but if we go past the terminology and look at your second question: "white forces black to make a move that gives black an advantage. Is that possible?", the answer is yes. You can even force the other player to checkmate you; there's even a class of chess problems called selfmates.
If you look up the meaning of "zugzwang" you will see something like
Zugzwang (German for "compulsion to move") is a situation found in chess and other games wherein one player is put at a disadvantage because they must make a move when they would prefer to pass and not move. The fact that the player is compelled to move means that their position will become significantly weaker. A player is said to be "in zugzwang" when any possible move will worsen their position.
So, by definition if there is only one legal move and it makes your position better then it is not zugzwang.