In the 2011/12, 2012/13 and 2013/14 seasons, Balotelli has recieved 4 red cards, and that's across ALL competitions, including internationals. Not a great record but definitely not the worst.
It's clear he didn't get on at all with Mancini, and the british media love to hype up that kind of thing. I reckon he'd be okay with Arsene, and I think he'd be a great striker for Arsenal tbh.