As a possible starting point.
What state are your batteries in? These cars are notoriously fickle unless the main battery is producing a healty voltage. In fact, one of the reasons the engine stop / start fails to work is that it detects a low overall voltage.
I can't say all the problems you mention would be connected but I'd certainly consider a new battery if you don't know the age of the present one and may have a bearing upon the faults you describe.The secondary battery has been known to fail but not as often as the main one.