First the battery drain. Check the emergency brakes are not being engaged. Second verify polarity on the battery connections, negative cable should show continuity to the frame. Remove cable, check with ohm meter. Then you need to trace the positive wire and any branch circuits for a draw. Isolate so you can check one circuit at a time.
GFCI issue next. Yes check neutral and ground bus are separate in the distribution panel. Since all breakers off does not help the first thing to check is the main cord. Check or disconnect at any junction boxes or the main panel to isolate the issue.
Post what you find.