The fuse could have blown because someone crossed some wires fiddling with something. If the new fuse doesn't blow then you are good to go.
The converter should keep the battery charged whilst on shore power.
I could run my pop up for 8 days dry camping. But we didn't use much inside, mostly just the water pump for showers and a few lights at bed time. I also had a small solar cell hooked up to it and plugged my truck into it at night. Make sure you run your fridge on propane, not 12 volt while dry camping.
You can buy an adapter that will screw on to the drain line that will accomodate a water hose.
Good luck and enjoy the new pop up!
2016 Ford F150 Platinum
2013 Coachmen Freedom Express 233RBS
Prior: Jayco Pop Up, Shasta Bunkhouse, Rockwood 2560G Pop Up