Stalemate means win if there has been a check
Ok, that makes sense. So the only "normal" draw would be no checks in a game, which then ends in stalemate. There might be other peculiar draws, like no checks, then 3-fold repetition, then 50 moves with no progress and no checks.
Would have to be. This draw rule favors the higher rated player so the opponent can play brilliant as black and then it's who gets checked first?!
Black just got handicapped to suit time. Don't play if you don't have time.