What Gates Carbon Drive parts should I upgrade?
Hard to give a good definitive answer to this. It's impossible to predict of replacing one or both sprockets and the belt will solve the rubbling and squeaking problem, although it's possible that upgrading to the newer type Gates belt would help (presumably they have changed the design because it was better).

If the rear sprocket retaining ring comes loose, something is probably worn badly, probably by riding when the ring came loose the first time.

The retaining ring really needs to be tightened to the proper torque specification with a torque wrench, which is may be way more than you are estimating.

If the sprocket spines are damaged the hub splines may be damaged too. I'd evaluate the hub before deciding how to proceed.