Does this tray fit in the factory console without modification?

Yes. It slides into the OEM console opening as-is. No cutting, trimming, or adapting required.

Will it stay in place while driving, or does it need to be glued down?

The gravity fit keeps it seated during normal driving. If you want permanent security, you can apply adhesive after test-fitting — but it's not necessary for everyday use.

Can I remove this later without damaging the console?

Completely. Since it's designed as a drop-in tray with no fasteners, you can pull it out anytime. If you used adhesive, carefully peel it free — no residue should mark the plastic.