On a bmw/mini...
There are two systems, RDC and RDW. (but which one is which I can't remember off-hand lol)
If the valve is metal bodied then inside the wheel is a sensor which transmits pressure.
If not its the good old system of looking for changes in wheel diameter through wheel speed. Think circumference getting smaller as a tyre deflates.
Run-flats can be repaired, but usually they need to be sent off rather than done at your average tyre bay.
As to the insurance question, I'm not sure you can claim that changing brand of tyre is something that invalidates your insurance, so long as the tyres are replaced with those of the correct size and speed rating. After all any wheel can be fitted with Run-Flat tyres and vise versa....
Alex