Are all KQvK positions winnable if it's not stalemate and Black can't capture on current move? Are all KQvK positions winnable if the position isn't in itself a stalemate and Black cannot capture on the current move?
Yes, all KQvK positions are won under these conditions (no stalemate, no capture). The same holds for KRvK. 

The only possibilities for such basic endgames not to be won under your conditions would be:


a piece has too few square available and can be captured by the black king (not immediately but in the next move)
white on the move cannot avoid stalemate (or material loss)


An example for the first case (black to move):

[FEN "7N/8/8/4k3/8/8/6K1/7B b - - 0 1"]


the second case (white to move) looks like this (to avoid stalemate, white's king has to go to the d file when after Kb7, black wins the bishop or knight):

[FEN "kB6/2K5/N7/8/8/8/8/8 w - - 0 1"]


However with the KQvK and KRvK, the queen/rook always have enough space to avoid these problems.