(a) Change of PIC mid flight?
A change of PIC in flight would mean that the first pilot volunteers to relinquish command, and the second pilot volunteers to take command. I don't think you can claim to be pilot "in command" if you consent to a situation where somebody can take control away from you as and when he/she sees fit. After all, that means you're not in command but the other person is. Or, in other words, the ultimate responsibility for the safe execution of the flight lies in his hands, not in yours.
As far as I know the only time where "safety pilot" is defined in legal terms is the situation where somebody has a license but lost his medical. In that case he/she can exercise the privileges of the license only with a safety pilot on board, who needs to be qualified and current on type, and there's a whole CAA leaflet out there on how and when the safety pilot is supposed to take over command.