2. The proficiency check takes roughly an hour and is simpler than the PPL Skill Test.
What I understand is that there's no legal minimum duration for the LPC. At my club the thinking is therefore that if you are very current (flown well over 12 hours in the last year) it's actually cheaper to book an examiner for an LPC than to book an instructor for the one-hour instruction flight, and then find an examiner to sign the paperwork.
Since the LPC doesn't include an actual nav section (but you've got to prepare a x-country on paper anyway, which will be checked), just upper air work (stalls, steep turns, PFL etc) and some landings (short field, flapless etc) the actual flying time can be as little as 20 minutes for the examiner to be satisfied.
5. If you approach the Examiner with everything correctly prepared and ready for signature, he/she would be greedy in the extreme to expect payment.
At my club they charge a nominal fee of 10 euros for the examiner to go through your paperwork. This is added to the normal instruction fee if the flight is an exam flight and not an instruction flight, and is charged as a separate fee for going through the paperwork and getting a signature in case of a reval by experience. As far as I'm concerned it's entirely reasonable given the time it takes an examiner to handle the paperwork, and given the time and monetary investment somebody has to undertake to become an examiner in the first place.