bypass valve

Yep - you know its working because your "hot" water won't be hot.

Yes you should... all you have done is disconnected the hot water tank from the flow.

It must operate this way so that you can winterize with antifreeze in all your hot and cold water lines EXCEPT the hot water tank!

My manual valve configuration routes the cold water inlet to the hot water outlet at the tank. So in my case, the cold water will run through the hot water lines.

Yes you will, but the water does not go into the heater, it just bypasses it.