1999 Sun Sport - Electrical Issues

[1999 Sun Voyager]

We are new...so please be gentle?

(1) Electrical issues began with the hydraulic leveler lights coming on while driving, but when doing a visual, the levelers were not down. Pushed "Emergency" button, then "off", then "on" to make sure the lights were indeed off & back to "off". (It happened once again when it was only idling, while parked.)
(2) Today we could not get the RV to start at all (Friday no problem)..and noticed the panel by the entry door, where we turn on the batteries, was "on", when it had been "off" when we left it three days ago. (The other thing we did on Friday was to turn on the furnace for about ten minutes.) We could not turn these switches to the "off" position today.
(3) Today when we tried to jump start the new engine battery, but it was draining as fast as it was charging.
(4) Today when looking at the house batteries, it appears the front one (puffy sides) was defective & we also thought maybe it was hooked up wrong but cannot find a wiring diagram anywhere to say for sure. (It has the short cables so am assuming it is not a parallel hook-up?) Only worried because there was a short black cable just lying beside the front battery.

There are so many places to start, but with this site FULL of experienced RVrs, I am hoping somebody has an idea of where to start??? We are replacing the one house battery with the puffy sides, hoping that will be it. ... Thanks ...