Just from experience. Single wall pipe should be a minimum of 18" from a combustible. It's extremely unlikely that you ever have any issues, but technically it's not correct. Either a pipe shield or double wall pipe is what would be needed to correct it. BK recommends double wall on all of their stoves for the best performance.How can you tell by looking at the outside?
The cat will not always glow. It's very dependent on the amount of smoke it has available to burn. It also will be much more active when its new, after a while it will be much more predictable.