Will this glass drop straight into my existing mirror housing?

Yes. This is designed to bolt into your factory mirror assembly at the original attachment points. No drilling, no custom brackets needed.

Do I need to remove the entire mirror from the car?

Depends on your comfort level, but many people can swap the glass without pulling the whole mirror. Test-fit first to confirm your approach before committing.

Is this just the glass, or does it come with the backing plate?

This is the glass lens only. Your existing mirror housing and backing stay in place — you're replacing the reflective glass surface.