Bad ground issues cause all these sorts of problems, all except the
draining issue, that must be a load problem, could be through the
alternator.
Remove all the fuses and check for a spark as you connect the battery
cable, or use a tester to detect a load drain, if you don't get a drain, start
connecting the fuses 1 at a time until you find it, and go look at the part
that is causing the problem, same can be done with the alternator, it's just
the plug on the back instead
Wild