Usually this is agreed upon in writing upon agreeing to move in. He needs to find that.

Depends on the area. In my area you pay a full months rent upfront as first months rent then on the first of the month after you move in you get a prorated amount.

Most areas also have pretty strict holding requirements if people prepare rent more than a certain length out, I doubt the landlord wants to deal with that.

It’s not uncommon but not the standard either. I’ve never paid last months rent. First month plus deposit for every apartment I’ve ever lived in