I'm glad my study and suggestion were helpful for you :)

Now my question is: There is no way for black if white watches out for stalemate, right?

No, the position is a win no matter what. Of course, there is still a chance for a player will spoil the win and force a stalemate, but in principle, there is no hope for the defender if a correct technique to win is performed.

And: How is the rules for a draw? It depends on the framework you're playing in, right? I heard of 50 moves, I heard of 3 similar moves. Where's some guidelines on this to find orientation and not pick a rule out of thin air?

Once you've got this material relation on the board: K + B + N vs K, you're forced to win up to the move 50 or earlier, because as there are no pawns and any other capture simply leads to a draw due to insufficient material, you're asked to prove the win in certain reasonable number of moves (50). In other positions, if you move a pawn or capture a piece, that resets the counter for the 50-moves-rule.

The other rule is the threefold repetition. You can't have the exact same position on the board three times, because that implies you've not made any progress and then it's a draw.

These rules always apply in chess regardless of the time control. Online chess websites watch out to comply with these rules. Maybe you could skip one of them in your informal games, but in general, you can't ignore them. You can find more information in the Laws of Chess by the FIDE.

Thanks for your puzzles, @eniolw. I'm enjoying it here and there a lot to be away from automatic online chess.

Nice, thanks!