1. Yes benching would improve. Just like anything else, practice makes perfect, and the more you do it (logically and with good form) the better you will become.
It is a common misconception that push ups have a hard limit when it comes to strength increase. Yes, if someone were to do just regular push ups (no changes in leverage) then their strength would...
Bodyweight exercises only will actually give you fantastic results if you perform them properly with good form. And you can make the exercises harder by decreasing leverage.