The burn can either be skin or ligs. The initial stages of hanging generally get the skin used to the activity, but when you get the attachment right the ligs will start to give a slight burn. In my experience, SD gives a burn just above the penis for the ligs attaching to the pubic bone, OTS pulls on the ligs that attach right at the back of the crotch, BTC always stretched the fascia in my lower gut.
I dont think fatigue is that important, it is better to be sensible, increase your weight and sets slowly and steadily, and be regular with your routine. I have had days where I havent wanted to hang, but its more because I wanted a day where I didnt have a weight attached to my penis, ie mental fatigue instead of physical fatigue. My MA teacher says it is better to train until you feel exhausted and you want to do more, this is where you stop. This will leave you with the urge to train on the next day. I also apply this to PE, and work.