1. I don't think he feed them anything. He first found them coated with ooze, already mutating, and took them back to his burrow. After that they all started mutating quickly and I guess he fed them anything he could find.
2. I don't know, rat's can get REALLY big. He knows the stealth art of the ninja, how do you think he snuck around?
There're lots of places to get food, if you aren't very picky. You'd be surprised what people will throw away.
3. Heh, I doubt that pizza was hot. Not even warm. Even a bit soggy, maybe. But then again, you wouldn't believe the perfectly good food people will throw out because they're full.
4. It's possible it was. Splinter didn't think about it right away, but he probably went back just a day or two later. It shouldn't have floated that far.
5. Well, since show is based on the Mirage books, we all (well, most of us) assume that Splinter took them from Yoshi's home/martial arts school.