What? No.

Q-Gears is a fairly recent reverse engineered FF7 engine. It's made by a couple of people and it's a non-profit project.

Mother 3 most likely used on a custom engine as back then it wasn't really necessary to use a well known game engine for console games. Besides, they asked some of the Pokemon Stadium guys to help them out with Mother 3, since they didn't know the first thing about 3D games (Which was one of the reasons why it got canned).

As for Final Fantasy 64 - it never existed. they had a small realtime cutscene demo, sure, but it ran on pc hardware. The game never really left the planning stages. There might be a build somewhere (Or might have been, as these things can die out completely), but in that case we don't know anything about it.