The clear line goes in your antifreeze jug, the valve, when shut, should make it draw from the jug instead of your fresh tank. The hose coming through the floor likely comes from the fresh tank.
As for the water heater I'd turn both valves the opposite direction and see if that bypasses the heater. Easiest way to tell would be drain the water heater, close the valves, then hook up the city connection and seeing if the faucets still work. If they do and no water runs out of the water heater drain you have your answer.
Let us know if you figure it out, good luck!
2016 Jayflight 27bhs Elite
2015 Chevy 2500HD