A few answers
I do not know your exact camper but most all TT campers are designed to run on 12 volts to be self contained when away from shore power. The AC, Microwave if you have one and 120 VAC will not work, but all other system should unless you have something special. The fridge can be run on LP gas but the controls run on 12 VDC and so does the HW heater.
Yes the converter does charge the battery if everything is connected and working properly, again unless your model has something special about it. The converter creates 12 VDC from 120 VAC shore power. When the lights and other 12 DC devices are on, it uses that power first, when any left over power is available, then that 12 VDC goes to charging the battery. Again if everything is hooked up and working properly.
On the roof, I have not done one of those yet, but the job is doable in my estimation if you are handy with wood tools. It will take some searching on the right procedures and if you have a rubber or metal roof. The manufacture of the roofing material can help I would think on how to apply there product correctly.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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