If he's doing it based on valuation models he's created and 10-Ks, why not. Might be a fun math exercise if he has money to burn.
How do you trade stocks with the amounts of money a typical 11 y.o. has?
Get a small business loan from your parents?
Loads of kids do that for things like a lemonade stand or a lawn mowing business during the summer.
I'm assuming an 11 year old trading stocks has parents that have money to burn and receives it from them, so this wouldn't apply to typical 11 year olds.
There are several brokerages that will let you buy fractional shares.