SIMPLE

There IS GRAVITY on the moon...just less than on Earth...EVERYTHING in space has gravity in the form of graviatation--i.e., the pull of everything in space on each other.

And, the answer to your second question is simple.

The FLag WaVED like that because there IS NO AIR...get it? It's called Inertia
**there is no wind resistance to STOP the flag FROM waving.
All they would have to do is Get the flag Moving manually and it would continue to move because OF the Lack of strong gravitational pull and lack of air.

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