The on board water pump will prime itself (self priming type of thing), you shouldn't have to worry about that. How long did you let the pump run while "gargling"? It may have just been the air in the pipes getting pushed out. Yes check for valves under sinks and in cabinets, there may be a winterizing valve still closed or set for bypass. I am sure someone here with a better knowledge of your camper will chime in.
As to the jack: When I am home, I use a large rolling floor jack to service the wheels. For on the road, I practiced a tire change using my truck's (F250) jack and it works fine. As mentioned previously, place the jack carefully to avoid any damage. Also, as mentioned, make sure you have the correct size wrench/socket for the trailer lug nuts! I bought a socket specifically for the trailer wheels, and keep it in the truck's glove compartment. I also have a pretty good tool kit I keep in one of the trailer's compartments.
See you on the road!
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2021 F150 2.7
2004 21' Forest River Surveyor