A good size mountain bike for a 10 year old is one that is around 24 inches. This size is good for kids who are just starting to ride mountain bikes and need a bike that is easy to control.
A 7 year old can definitely ride a 24 inch bike. The bike will be a little small for them, but it is definitely doable. They will need to be able to reach the ground with their feet and be able to pedal the bike. If they can do these things, then they should be able to ride the bike.