You do not need to close the loop, they can just be plugged. If you aren't going to ever need heat in the rear, I would plug them at the engine and tear out the whole thing. At the engine you can either cut the hose and stick a plug in, screw out the fitting and screw in a plug (if it has that kind), or just make a small loop from one to the other. If you do any of that remember, you will have to drain the coolant to do it. (not onto the ground coolant is poison)
coolant still needs to flow through
It doesn't, unless there is another heater that it is supplying. Without seeing it, I would guess there are some "Ts" somewhere that go to the front heater/defroster
I'm sure the small "tube" is just the electrical wire to the heater fan, probably inside of some sort of insulation.