My question is, Can I lay stone Tile directly over the Formica Top? Is
there a proper adhesive designed for applying stone tile directly over
the Formica?

I wouldn't. I would rip the formica off than replace / repair the
plywood and put a thin hardyback board on top before tiling.

While the formica is off I would check for alignment and secure
fastening to the wall and between cabinets.

But that's me :)