When doing the driving theory test at the test centre are you given/allowed to use: 1) a calculator 2) pen + paper
Neither I'm afraid. The only things you take in with you are your licence photocard and a key to the locker where you stuff everything else you're carrying. You can mark individual questions using the software and go back to review them if you want, but apart from that you haven't got anything else.
But as a new driver, learning the distances. It is good knowing how to work it out in order to remember
You should only ever be asked one question about braking distances, and it's never anything you'll need to know in your driving career because of how archaic the highway code is. Nevertheless, the calculation is easy enough to do in your head.