Standard procedure is to sell a car with number plates on.

I do not know what happens if a buyer is from a different city...?

As far as I remember if you have special/qool number plates (or your simply love your number) you can keep them however it makes the procedure more difficult and at some point it is more expensive (do not remeber for whom - buyer/seller).

Do you already know how it works with your insurance coverage when you sell a car (AC/OC - TPL/casco)?