you now know the source of your pump cycling on/off. Do your best to seal the leaking plug. If you are still worried about the cycling pump, then only turn your pump on during the night if someone has to use the bathroom.
as for propane use, start a weekend trip with a full tank. make a mental note of what LP appliances are used during the weekend (WH, stove, furnace, frig). refill the tank again after you get home. that will give you an idea how much LP gas is used and an idea how long your tank will last.
I have a 1gal portable tank that I use for my 3burner coleman stove. It will ALMOST last (2) three day weekends of eggs, bacon, frenchtoast, coffee, dinner and hot cocoa for my family of seven. therefore I fill it before we leave everytime.