Cracked flues can be tricky and the popular answer is that it suffered a sudden thermal shock such as a creosote or "chimney fire". What you must rule out are damage prior and during construction such as mishandling and seismic events. One cracked tile alone may be from construction such as kicking the tiles off the delivery truck or dropping them. However, longitudinal cracks in the corners are more indicative of thermal shock. The fact these cracks extend from one tile down to the next would seem to fit the thermal event vs. mishandling. Seismic damage is Dale's specialty since he lives out there so I'll defer to him on that. There appear to be dark stains in the cracks, which would indicate creosote deposits while the tile opens up during heating much like a clam shell. This would seem to indicate there was the initial event then continued use afterwards.
Chimney fires are rarely reported or observed by homeowners. They tend to last about 20 minutes so you could be in the shower and never know it. Often, the homeowner notices the chimney is suddenly filling the house with smoke where it used to draw just fine. They call a sweep, who removes a huge plug of pyrolized creosote. When creosote burns, it can puff out like a croissant, blocking the flue. Many sweeps are keen to spot this though some aren't. Let's say this chimney was swept. If there is no rain cap, the water can rise the creosote off much as you see here. BTW, wet creosote run off can seep into those cracks without needing heat to induce enough hoop stress to open the clam shell.
Yes, that 8x8 thimble is protruding into the flue. It should be cemented flue with the inner face of the flue wall. It also appears to be damaged.
So, was this taken at the top of the chimney? Are you telling us this is a 6 foot tall 13"x13" chimney? That's a functional problem right there as it is way too short to generate sufficient draft. What about roof clearance? A woodstove with a 6" collar cannot vent into such an oversized flue. Doesn't appear to have a cleanout either.
I'd recommend a Level II inspection. They would be a lot better off if they tore this chimney down and replaced it with a listed factory chimney of proper size and height.
HTH,
Bob