Le Chaud Lapin writes:

What is the definition of a stall anyway?

An abrupt loss of lift.

I'm saying that, if you take a plane with certain critical angle,
throw away engine, put on an engine that can generate 10x the thrust,
the plane should still fly, even if you exceed critical angle.

No, the thrust of the engine doesn't matter, unless the engine itself is
supporting the weight of the aircraft with thrust (possible in a few fighter
aircraft). A wing above the critical angle will stall at any speed.

These books imply that the critical angle is angle at with bad things
happen above the wing, and because of that, the plane will fall.

Yes, true.

I'm saying that, you can have all the bad things happen above the wing and
still be able to keep the plane aloft due to compression that occurs
beneath the wing.

The wing is not supported by compression. It is supported by the displacement
of a mass (of air) downward. If this displacement ceases to take place, lift
disappears. A stalled wing does not divert air downward, so it doesn't
generate lift.