It is perfectly fine to stay hooked up for onernight stays. If you traveled through the night or parked it for the night, it would be hooked up. Absolutely no problems. As above, it should be level.
Yes, you can use propane for fridge and for water heater and 12V for water pump. If staying more that a day or so, you run the risk of draining your RV battery. I usually do not stay hooked up to my TV because I do not want a dead truck battery. GM is live all the time. Ford only when key is on. I would think about another 12V battery or at least two 6V batteries to give you more amps. You could also get a small inverter generator if you will boondock in a place where they're allowed. Hope this helps.