The valve most likely is the winter bypass for the hot water heater. When in the bypass mode no water will go into the heater and while you are winterizing any blow off will bypass the heater and purge the lines.
As for that rubber hose a picture would help.
There is a drain hose from the condensate tray in the frig but I doubt that the frig is above the heater.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles