Hi here are some useful free websites for playing and learning:
Lichess is great for playing and learning you just need to ensure that you select the Child option rather than the adult one when setting up the account. This is very important and will keep your child safe.
Kids chess is also great and the free membership allows you to enjoy some of the features (but the paid version is recommended if your child is serious about chess):
The Exeter Chess website is an excellent one and probably the best single place to get free material on the web:
Most of the material is old but still useful for a child.
Chessity is a good alternative place to learn (particularly tactics):
Most of the top Dutch Grandmasters learned via the method used in Chessity: loads of small easy tactics. You need to pay for most of the functionality on this site.
If anyone needs any further information or wants to know about other sites just send me an email at: firstname.lastname@example.org