Is df size connected with moon size or is it just random?

It's just random.

thanks.

One more question. if I've got very small moon, is there any chance that if I continue with moonshots on that planet new bigger moon is created, and replaces this small one? Is this possible, and if yes what happens with buildings, or should I first destroy a moon and then try again?

You have to abandon it first.

Weresloth wrote:You have to abandon it first.

That is correct. No planet can have more than one moon.