do i leave the batt switches on when on shore power

Connected to shore power is one means of having converter recharge.maintain the charge on batteries. IF they are not switched off.

And YES.....if they 'look toasted' then that converter overcharged them because it isn't a three stage charger and the water boiled out.

Need to take them out and have them load tested...any auto parts store.
Then when you buy new batteries....buy a new smart converter/charger and replace your old dumb converter