I'm giving my old iPad mini 2 to my son. He played games on it. Is it possible to erase the iPad, create a new user (my son) and then install the previous game apps with all their data?

Ideally, to properly erase the iPad and prepare it for a new owner, you should follow this procedure:

What to do before you sell, give away or trade in your iPhone, iPad or iPod touch – Apple Support

This procedure will erase all sensitive data and locally stored files - returning the iPad to a clean-slate from which it can be setup from scratch using a new AppleID for your son. Don’t fall into the trap of sharing an AppleID; this you will regret as you encounter issues of unintended data sharing and potential account lockout.

If you setup Family Sharing, you will be able to share all existing and future purchased Apps between Family members. Once the family group can been created, you can simply download these Apps from the App Store without needing to purchase them again.

Your only problem is being able to selectively save the individual game data - and restore it to your son’s iPad. Some games store associated data in its own cloud-service account - whereas others save this data locally on the device, or perhaps iCloud. You need to establish where such data is stored, as this will inform the necessary actions (if possible) in transferring this data - effectively between users.

Here are a number of resources and support pages that should be helpful:

Use parental controls on your child's iPhone, iPad and iPod touch – Apple Support

Use Screen Time on your iPhone, iPad or iPod touch – Apple Support

Set up Screen Time for a family member on iPad - Apple Support

Family Sharing - Apple

Set up Family Sharing – Apple Support

Share App Store, iTunes Store and Apple Books purchases with Family Sharing – Apple Support

How to create a new Apple ID – Apple Support

https://www.imore.com/how-set-up-family-sharing-iphone-ipad

Games and other downloads are forever tied to the AppleID used

to acquire them. You could try contacting the developers of each

game for assistance, but such a transfer from one ID to another

probably will not be offered.

Family sharing would allow him under his new AppleID to use

items from your AppleID (if the developer allows sharing) but the

data, levels, etc may not be accessible.

https://www.apple.com/icloud/family-sharing/

Here is what you need to do before giving the iPad to him:

 https://support.apple.com/en-us/HT201351