A) A flight instructor is not allowed to give lessons ad-hoc, unpaid or not. If it's PPL studies training must be performed by a RF = Registered Facility, or if IR och CPL a FTO = Flight Training Organization.
B) Only aircraft registered on the RF or FTO permit are allowed to be used for training. (which a whooping charge for the privilege of placing a AC on the schools permit - negating any savings).
That is true here as well but it applies only to training required
for the initial award of a license or a rating.
So if you do say a PPL or an IR in your own plane, that plane needs to be "put on" the FTO's fleet. It is a simple piece of paperwork but still most FTOs won't touch it because they make more money flying their own ones, of course.
All other training e.g. recurrent training, or training towards a PPL or an IR skills test
once the required hours and syllabus have been covered at an RF/FTO, can be done with a freelance instructor.
The freelance-instructor hours can be logged openly in your logbook (provided he is actually an instructor
) and you can pay him if he holds a JAA CPL. But those hours cannot be used towards the 45hrs of a JAA PPL, or towards the 15/50/55hrs of a JAA IR.
Maybe Sweden has a ban on all instruction in customer-owned aircraft but that is simply mad. In that case, fly your plane here to the UK and do it here
There are also schools in Spain where you can do it in your own (EASA reg) plane - FIS at Jerez for example.
C) Since the RF or FTO are charging for the aircraft it's commercial and the aircraft must be "public cat" maintained i.e. newer than 12 years engine under a maintenance contract with a CAMO.
That is quite possible.
To be fair to the PPL and IR examiners, they have to climb into various wreckage, once or twice a day, and much of the FTO wreckage is only barely airworthy, so even though there is not a good engineering reason for taking an engine apart just because it is 12 years old, they probably like to draw the line somewhere
If I was doing that job I would be a lot more fussy about what I climb into.