Probably double gasket on filter due to the old one stuck to mounting surface on engine when old filter was removed. That would quickly drain the engine oil and happens frequently.
You disconnect a battery on a running modern engine you can foul up the ECM and other modules beyond repair, it might operate, but damage will be done. Not the intended or proper order of operation.
No , they run off the battery, the alternator is for replenishment, you are correct about the battery being a filter, but that is for unexpected demands to reduce surges.
The last good engine in a Wrangler was the 4.0 after that pure crap when Fiat took over. I thought Diamler was going to be bad, but Fiat trashed reliability the breed. Europeans build nothing but compromise.
I would have the pan dropped and fluid and filter replaced soon. I personally change fluid and filter every 25,000 miles regardless of manufacturer recommendations because as they say many of the fluids are for the life of the transmission, trans dies, there's it life. You cannot over maintain...
The only time any of this oil is a problem with catalytic converters is if you are burning a ton of oil, that is the only concern. Otherwise use whatever you want.