Question

1. The children lay down on their stomachs.

2. The children lay down on their belleies.

3. The children lay down on their fronts.
(Which expressions are right?)

4. Lay on your right side on the floor.
5. Lay on your left side on the floor.
6. Lay on your front side on the floor.
7. Lay on your back side on the floor.
(Can we use like this? Do we have to delete 'side'?)

Answer 1

First, learn "lie" versus "lay".

http://www.quickanddirtytips.com/education/grammar/lay-versus-lie

"stomachs" and "bellies" mean the same thing. "Belly" is informal and not as polite.

No, you do not have to delete 'side". We do say "left side", etc. "Backside" usually means one's buttocks, though. "Back" and "front" don't require "side", but it's not wrong.

Answer 2

I corrected the errors. Thank you.

1. The children lay down on their stomachs.

2. The children lay down on their belleies.

3. The children lay down on their fronts.
(Which expressions are right?)

4. Lie on your right side on the floor.
5. Lie on your left side on the floor.
6. Lie on your front side on the floor.
7. Lie on your back side on the floor.