I exercise Exempel by teaching him tricks or jump over hurdles. He also has lots of toys and I usually put treats in them so he has something to do for a while. During summers we're also outside a lot and exploring the woods or something!
I've read that they should be outside of their cage a minimum of 3 hours/day, but I'd say they should be outside of their cage a lot more than 3 hours/day.
#2 Not automatically, but they are easily trained since they generally do their business in a specific place, often in a corner. Just put a litter box in that place, and if accidents happens outside of it: you just move that to the box, and they will learn. You do need one litter box in every room the rabbit are allowed in though, because they can't hold it in for long. And clean it often, because they will do it somewhere else if it's too dirty. Of course there are exceptions, some will never learn.
Also, they often poop while eating, so many have a hay rack above or beside the litter box. Then the rabbit can sit in the litter box while eating. （＾ω＾）