Hey, glad you're enjoying the game! All save files transfer naturally between updates without you having to do anything - although Android sometimes doesn't play nicely with Ren'py so you might want to backup your save folder before updating if you're not on PC, Linux or Mac.
1. No items available just yet, sorry! They will be introduced when I add the "Bar/Club Date" content.
2. Yup, those are the current maximums.
3. There are enough rooms for all the girls, but who exactly moves in will be up to you... right now, though, nobody is ready to move into the manor. Maybe soon, though...
4. There's no "battle system" in the game, but there are certainly people who don't have your best interests at heart...