JeroenC,
The first question is very easy to answer. The answer is on page 40 of LASORS, in Section A Appendix B, which contains a table showing how to log flight time. Row J of this table covers a "Pilot undergoing any form of Flight test with a JAA or CAA Authorised Examiner" other than a test for a co-pilot. For a successful test, the holders operating capacity is "PIC U/S" (Pilot In Command Under Supervision), and the timer is entered in the "P1" column and certified by the aircraft command (i.e. the examiner). Because you log it under the "P1" column, it counts towards your P1 total, even though this is not what you write in the Operating Capacity column.
The second question is much harder - it's one of the few cases which is not covered anywhere, and the CAA will evade any questions you ask them.
Logic says that PIC U/S would work. After all, you are capable of acting as P1, it's just that you are being supervised. But according to LASORS, there is only one time you can log PIC U/S on a single-pilot aircraft, and that's a successful flight test. So that rules out the logical answer.
There are two options left to you. Option 1 is that you log P1, and your instructor doesn't log the flight at all, he is just a passenger. Option 2 is that your instructor logs P1, and you log PUT. This must be agreed beforehand between you and your instructor, because it has a big bearing on what happens, for example, in an emergency. Say the engine goes Bang while you're at the controls and you pick a field to land in.... if you are P1, your instructor might advise you that there's a better field over that way, and you may choose to take his advice, but the final choice is yours since you are the aircraft's commander. On the other hand, if your instructor is P1 and doesn't like your choice of field, he has the authority, as aircraft commander, to instruct you to use a different field, or to take the controls from you. Obviously this is not something to be discussed when it happens - you must agree beforehand who is in charge.
FFF
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