so sorry to hear this, I am just about to have my cast off, but I am an adult.
I saw a little boy, about same age, with 2 casts like you describe, in hospital when I was getting Xrayed. He kept saying 'Down, down!' and the dad was saying not a chance.
Opportunity to play with remote controls, mobiles and other forbidden objects would get my child wiggling fingers. Interesting textures like playdough -- or you could manually wiggle his fingers for him, playing This Little piggy games, make it fun.
Lots of pillows for sleeping? Can you sleep next to him?
To keep cast dry in bath, get a bread bag or any long small plastic bag and cut hole in bottom, slip over entire arm, use rubber bands to keep bag over cast while he has quick dip in bath. Or just sponge clean him for a while (probably what I would do). Is cast fibreglass? Mine can get wet on outside fine, it's the padding inside that would get skanky and heavy if it got wet, that is the problem about keeping it dry.
How long will he need cast on?
I'm afraid you'll find he's stuck in pushchair a lot for his own safety because he can't put both his arms out to break falls . I would use reins a lot so that I could effectively break his falls for him.