Is the mass gain of celestial bodies really the reason why they slow down & expand their orbits?

Answer 1

I suppose it could have some minuscule effect on their motion, but I would say it is more orbital mechanics and the fact that no orbit is perfect. All orbits will eventually decay or expand over millions and billions of years.

Answer 2

Having a planet or moon gain mass by, say, meteor impact, can either increase or decrease its speed and increase or decrease the size of the orbit, depending on the trajectory of the incoming meteor. In general orbits don't change much.

The Moon is moving outward because of tidal coupling with the rotation of the Earth.