Is it possible that Mercury was once a satellite of Venus?

There is no evidence for that hypothesis.

Sure it’s possible. But doubtful. Given the relative mass of Mercury and Venus, for Mercury to have been a moon of Venus would have put Venus in a very odd orbital pattern.

No.

No, but it is possible Earth has lost something, wayyyyy back.

Actually, Earth has temporary extra moons frequently picked up, then discarded. They wait for us to come back around, then try again.
We have a jealous moon, and she refuses to allow hitchikers to ride along very far.

No.

Since Venus is in the Alpha Centauri solar system, it seems unlikely that Mercury would have been pulled to our sun, but rather to the sun in Alpha Centauri. Other than that, it is a feasible enough theory.

No, Venus is not in the Alpha Centauri solar system.

ROFLOLL!! Alpha Centauri is the star closest to our solar system. It is also a sun. Actually 3 suns.

The sun is our closest star.