Well, went and bought another battery cable today and properly wired my batteries in parallel and here are the results:
1. Replaced bulbs that burned out.
RESULT: All working fine. None of the lenses showed any signs of overheating. Guess that fortunately they burned out before any damage occurred.
2.Changed bathroom fan fuse.
RESULT: Operates normally.
3. Leveled trailer, turned on propane tanks and fired up refrigerator in propane mode.
RESULT: Heard it ignite and then went outside and could hear burner running. So it appears to be ok.
4. Turned thermostat up on heater.
RESULT: Heater ignited and fan came on blowing heat through the vents.
5. Tried my tank meters.
RESULT: Seem to be working normally.
Couldn't fire up the water because I'm still winterized and need to get to a water supply but hoping and assuming that's ok as well.
So, all in all I hope and think I dodged a bullet here. Could have been a lot worse. Just supports the reasoning behind completely checking out your systems before hitting the road whether your trailer is new or older. Had I just taken off with my new (slightly old) trailer would have been a disaster.
Thank you all for your calm support and advice. It's truly appreciated and I hope I can help someone here in the future. I'm sure I'll be back for more advice in the future. Nice to know you folks are here. Again, sincere thanks.