I dont think you would want to shut off the trailer battery while towing. If it's disconnected it cannot activate the trailer brakes in the event of separation. I would think if it has a shut off, it would be for when the trailer is stored to avoid parasitic losses draining the battery.
As far as the black tank, I would not necessarily trust the gauge, they are not known to be reliable.
I would shine a flash light down the toilet and hope that there is only a small amount of water in there and that the previous owner didn't leave you a half tank of their "stuff".
2016 Bullet 274BHS
2015 Silverado 1500 Double Cab
Andersen WDH