Chess Elo Calculator

From the rating gap: 1 / (1 + 10^((opponent − you) / 400)). A 400-point gap works out to roughly a 91% expected score for the stronger player.

FIDE uses 40 for players new to the rating list, 20 below 2400 and 10 at 2400 and above. Online sites use their own values, so pick the one matching your rating system.

Yes, when your opponent is rated lower. Against a weaker player a draw scores less than your expected score, so your new rating comes out lower.