And set a custom image like in steam Add non steam games ?

No.

And no.

Or optimistically: not yet.

It was possible through some workarounds, unsure if it still is. Still, it would only be useful as a launcher, no Galaxy features would be available for those games. Unsure about chat and fps counter, those weren't there when we were testing about adding non-GOG games to Galaxy.

Edit: 2015 thread, 2016 thread.