Regarding the "Play with the machine"

We know that chess positions are often times logically drawn. There is no further progress to be made over the board and humans would agree to a draw. When playing against the lichess AI, we humans are stuck when such conditions arise. There is no option to claim any draw and the AI will kind of move forever, wouldn't it?
Maybe a cool new feature on lichess that allows to offer draw to the machine and it would logically respond?
I love my dignity a bit too much to press the resign button on drawn positions, which I sadly had to do the last time around. Otherwise the "1 game in play" notification would keep annoying.

+1.

If the player holds an equal or better evaluation for N consecutive moves, it would be cool if the machine could accept (or even make) a draw offer.

You had a good idea anjeshkafle ! It's could be cool !