My first thought is to return to the standard hose. Does adequate flow return with it in place? If yes, further inspection of the heated hose is needed. If not, then the previous suggestion about the inlet screen is a good bet. If the screen is missing or damaged, junk may have become lodged in the onboard pressure regulator or one-way valve.
The pump has me stumped unless the FW tank isn't as empty as you think. The city water should tee into the high side of the pump. Turning the pump on draws water from the FW tank and applies pressure to the high side equal to the output of the pump. If the city pressure exceeds the pump, the pump won't come on. If you are certain the FW tank is empty, then someone may have plumbed the city water to the low side of the pump and installed a one-way valve to prevent the city water from flooding the FW tank. I'm just speculating on how the pump might increase pressure without water in the FW tank.
Air Safe Hitch, Reese Dual Cam 800#, Centramatics