Will this bolt straight to my existing bumper cover?

This bracket mounts at the factory attachment points on the vehicle frame. Your bumper cover clips onto the bracket once it's in place — the bracket itself doesn't bolt to the bumper.

Do I need to remove the whole bumper to swap this bracket?

You'll need to detach the bumper cover to access the bracket mounting points. Once removed, unbolting the old bracket and bolting in the new one takes minutes with basic hand tools.

What if I only need the left side — will my car still be balanced?

If your right side bracket is still good, running just one new bracket on the left works fine. The bracket supports bumper positioning; both sides don't have to be replaced together unless both are damaged.