The cars electrical can do strange things if it is a weak battery or connections not clean & tight.
As 2kg4u mentioned a ground check from battery terminal or adding a larger ground from the battery to body wont hurt either.
I prefer to not use the DIC for voltage readings as they are not always accurate.
Do you have a decent voltage ohm meter? If so, what are the volts reading, when car off, and when running?
To relieve battery worries, I would recommend that you have the battery load tested.
When it is time for a new battery, consider one of the newer more powerful styles of AGM type batteries.
They typically are 900CCA plus, are sealed and wont ever offer corrosion to terminals or wires.
Exide Edge makes reasonably priced ones, I just installed one in my 4x4 and run an Odyssey in the Buick.