If you run the stove on high and the wall gets dangerously hot, it is not installed correctly. 16 3/8" is required behind the stove. I would say that there could be an issue with the stove, but I can't imagine what would cause just the rear to be blazingly hot on low heat. Missing firebrick could maybe contribute.
@Ashful ? (He has 2 of your stove burning in his house.)
Please post us some pictures of the install, and the stove inside and out.
I would say your gunky glass sounds very much like a difference in wood moisture. From what I gather, the Princess will have dirtier glass than your stove burning the same fuel on low settings. That is not a serious problem though, and the hot rear wall is. We can troubleshoot the glass after the hot wall.
Don't worry about the cat glowing or not. If the thermometer says active, it is.