if i get my child an apple id, can i give him the apps i've already purchased for him under my id?

yes u can u can re download apps u have already paid for or free apps

As erman said, yes. Just not that your child will have to log into your account to update any apps purchased with your account. Also, if there are apps that need update from both accounts you can't Update All. You have to update them one at a time until the remaining apps were purchased from one account.