Are cartoon games suitable for children?

Many are, but the tag describes art style rather than age rating. Look at the game page and try it yourself first if the player is young.

What kinds of games are tagged cartoon?

Racing, jigsaws, brain teasers, board games and coloring all appear. The art is the shared feature, so use the category links to pick the type you want.

Do they work on tablets?

Yes. Most use simple tap or drag controls and run fine in a tablet browser. Larger screens are especially comfortable for jigsaws and difference games.