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Gravity is not a force. It’s just tensor warping, which manifests as acceleration in our paltry 3d realm, which you experience as a force.

Similarly in the falling lift there is no force making you float, just an apparent relative acceleration that you experience as a force.

General Relativity states that gravity and acceleration are equivalent, so yes, they cancel out. Unless you look outside you cannot tell whether you are in an elevator standing on ground on Earth (1g), or in space accelerating upwards at 1g.

It does because the frame is not inertial. There is a fictitious force “pushing you upward” because the elevator is accelerating downward. The fictitious force pushing you upward perfectly cancels the gravity pulling you downward and you feel no net force inside the frame.

I do not find anything at fault in saying it cancels out. Possibly you are too strictly affixed to some notions?