>>>Side-note: I noticed that the cold water valve doesn't actually open or shut. I turn it to the left it doesn't move, I turn it to the right it doesn't move, however the cold water is still getting to the washing machine fine. Do some valves work like this? I really don't know. How is my washer magically getting cold water?<<<
Your valve has gotten struck from not being used.
Most brands of wash machines want them turned OFF when not in use.
Put in one of these and you can turn both off by moving a lever.