Have the option to allow forced moves to happen automatically

Have the option in games (live chess too) to allow forced moves to be made automatically. A warning message would alert you to the fact that forced moves had been made on your behalf when you return to the game.

Or when you are going to win and the opponent's king has one legal move?

Yes, any position where there is only one move possible, you don't have to be in check necessarily, although this is more usual.

e.g.

and this would be an exception in any case - whites only move is to promote a pawn - however which piece the pawn gets promoted to could not be chosen automatically.

This was suggested ages ago but I'm pretty sure was deemed low priority due to the relative infrequency of its occurrence.  I'd still support it, but I'm sure that many players would want to have the ability to turn it off which is a reasonable request.

It sounds cool but I think I wouldn't use it much because it takes away the process of me finding the move myself.

if my opponent has forced moves, i just make my premove or conditional move (for live chess and online chess respectively). yeah i still have to wait for them, but all my next moves are already there for them to respond to.

 Good observation and solution. Well done.

I would hope, if this were imlemented, that it would be an optional control given to the individual for whom the moves would be made.