It's your call on the full tank sensor. Those sensors constantly malfunction, I would save the time and fuel and not go back just for that repair. In short time, you will not need sensors to tell you how much is in your tanks, you'll know, you get a feel for it.
There is a thread on cleaners for the tank sensors. Read the GEO method.
https://www.rv.net/forum/index.cfm/fuseaction/thread/tid/28874286/print/true.cfm I always dump my tanks prior to hitting the highway.
You will find it an easier tow to run with your tanks empty and just enough freshwater that you will need. I don't run a full freshwater tank , I carry 10 gals and fill at state parks prior to setting up.
Re the battery, either way, you can pull it and put it on a trickle inside or leave it on the trailer, plugged into shore power, the trailer converter will smart charge it . I have been doing it that way since 2004 using PD 9000 and WFCO converters. They both work and get the job done but I think the PD units are more popular units using charge wizard type technology. People usually upgrade to PD's not the other way around.
Good luck with your new unit and have many safe miles of travel .