It looks like they have followed the correct process, the answers to all your queries can be found here:
https://www.mot-testing.service.gov....als/class3457/
Remember that prescribed procedure is that repairs cannot be done during the test. If a defect is found, they have to fail it, repair it, and re-test. Even a bulb.
Also the MOT tester is likely not to be the mechanic doing the service and other work.