Re: Silly Question - can you remove/swap batteries from the car if it's running?
Used to be able to do it in the old days with a 37A alternator and dumb electrics but back in the early 70's I did some tests for the SCCA relating to kill switches and saw spikes over 200 volts if you disconnected a battery while charging.
Reason is simple: ELI the ICE man. A battery is like a big capacitor. Disconnect the battery while at a high charge and suddenly the amps go to zero and while the field is collapsing, the voltage goes through the roof.
Modern 100A+ alternators and fragile electrics just make this worse.
So before swapping batteries, shut the engine off.
Note: you can generally disconnect jumpers with the engines running because each still has a battery in the circut.