You seem more than somewhat confused. Your initial post refers to P to F aircraft and then you start quoting stuff relating to C of A aircraft.
The general principles are related to the purpose of the flight. What follows is broadbrush and does not cover every combination of factors.
Under the ANO if any payment is made other than for the services of the pilot it's Aerial Work and the a/c has to be maintained to PT standards.
If you are the owner of the a/c you don't have to pay anyone to use it and if you pay in instructor it is a Private Flight and not Aerial Work.
If the a/c is jointly owned then you pay the group for the use of the a/c and if you then also pay the instructor it becomes Aerial Work. Since a P to F a/c is not maintained to PT standards it cannot be used for Aerial Work. It therefore follows that you cannot use a jointly owned P to F a/c for paid instruction. The ORS exemptions allow you to pay an instructor in certain circumstances without making it Aerial Work, thereby permitting instruction in jointly owned P to F a/c.
The exemptions relating to C of A aircraft are there to permit paid instruction in C of A aircraft that do not meet PT standards, e.g. if they have an engine that is being run "on condition".
As to where the training takes place, that's down to the PIC, which in the cases envisaged by the exemptions is the Instructor.