Q: can my child only get free apps on his id

If his/her Apple ID has Credit Card Attached to Apple ID yes he can Purchase Paid Apps

Or you can go to Settings > General > Restrictions & Toggle OFF In-App Purchase

So he cant Purchase Apps

If I were you, I would carefully consider Family Sharing - Apple Support

I've read in these discussion the "children" have run up thousands of dollar bills with in app purchases. Family plan is the way to go.

Robert