Cracked tiles are a non-issue with coal, interior or exterior. The cracks mean nothing unless the tile stack has cracked to pieces and is collapsing - such as from an earthquake, intentional demolition, or a faulty (completely unvitrified) liner installed low in the tile stack. Stack is under negative pressure along it's length. A few cracks in an otherwise intact tile stack (hint - one or two vertical cracks - they were probably installed that way) is barely an issue /w a wood stove and irrelevant with coal.
The "chimney professionals" who see a crack or two in a tile liner and claim it's "unsafe" now with the for-profit backing of the CSIA et al. need to be taken out and smacked around; If you don't know how a chimney works or understand your trade - get the HELL OUT
That cap didn't look too bad; there's not much actual corrosion on that one. Coal attacks stainless four ways - very low o2 in flue gasses prevent replacment of passivation layer, Chlorine/HCL attack (coals contain significant chlorine), Sulfur/acid attack, and perhaps most importantly, what allows all these things to come together and work rapidly, is iron pitting corrosion from the iron in the coal fly ash.