A and C, as Genghis says, putting your C152 on a Public C of A could be difficult. I did it with an Aerobat and all it cost me was the price of fitting a starter motor warning light plus a fee to the CAA. This was done during an Annual inspection to make it all easier. If you get an engineer to look at the logbooks and the aircraft (which is advisable before buying an aircraft anyway
) he should be abnle to assess what remedial work is necessary to make the change from Private to Public Cat.
To get around the instructor problem you could rent the aircraft to your local friendly flying school and then pay the instructor through them whilst using your own aircraft. In the agreement you make with the school you can then specify what do's and dont's will apply to the rental of the aircraft to others. You might even make some money out of it