Does plugging a one way HDMI cable in the wrong way damage the cable Example The cord has arrows pointing a direction with the words Signal Flow after them and I plugged the cable in backwards?

You won't damage anything, but I have found some cables to be unidirectional. I thought it was absurd, and completely contrary to how cables work... until someone suggested it with a specific setup between a computer and a projector and sure enough it would work one direction but not the other. I've since discovered other cables that also are unidirectional HDMI cables.