You don't need water pump on while hooked up to city water. You should put some water in FW tank for those times when water is shut off at CG due to repairs.
Leaving gray water tank valves open is personal preference. Black water tank valve should remain closed until toilet burps, then empty and rinse.
Sewer hose support is also personal preference. Since your RV will not be moving off the spot try to keep all your hoses and cords tidy and out of the way as much as possible. Makes it easier for the folks with the weed whackers.