-Do you start your engine with both batteries?
Not normally, if batteries are low you may need to. Usually have a designated start battery(#2 in my boat)
-Do you run the engine with both batteries selected so it will charge (or will both batteries charge even if only one is selected)?
Both batteries will charge in the both position, but I prefer to switch from 1 to 2 at scheduled time intervals while running the engine.
-While sailing, or not using shore power, do you use just one battery?
Yes, I use the house battery(8D) and leave the start batt. for starting only.
We have a switch like yours and routinely switch from #1 to #2 while the engine is running with no problem so far(15yrs this boat, Yanmar). Normally you will have one starting battery that is a heavy duty diesel starting battery and then a second deep cycle "house" battery that you use for everything else. Hope this helps. John
SV Laurie Anne
1988 Brewer 40 Pilothouse