hi, i did my assessments in Swindon a few weeks ago. so to answer your questions:
1 - all the pens/pencils/erasers etc were provided on the desk when we went in. They didn't mention anything about using your own but if you need to you can just ask. They are very friendly and accommodating.
2- if i recall correctly they asked us not to write on the info sheet for the TRP test because they wanted to re-use them. so its notes only.
3 - the order we did the tests off the top of my head (i might have missed some):
- Group bourdon
- bleep counting / scanning the phone book
- TRP rules test
short break then onto the computer tests
- perception test / spot things in the traffic scene pictures
- 2 hand joystick test
- the vigilance / stare at the grey square for 30min
After everyone finished the vigilance we did a situation judgement exercise on the computers. Its not a pass/fail test on its own and its not timed but they said it feeds into the MMI and your answers will be considered in the overall decision of pass/fail.