That fireplace should be inspected as Dale said and expect some expensive repairs. That damper ajar will cause severe turbulence in the throat which can lead to spillage. Whoever installed that 13"x13" Lock Top damper was supposed to remove the old damper's valve plate first.
This chimney has undergone a major repair. Since the mortar lines don't start on one course but are staggered, my guess is there was a collapse or blunt trauma such as lightning or tree hit. The concrete crown is nice but they should have an expansion joint btw concrete and flue tile to allow for thermal expansion yet seal out water. From the cracks in the flue tile, I would venture a guess they did not have any sort of rain cap on for a few seasons, which lead to freeze-thaw damage. With that little walkway next to the chimney, I would probe the soil to find the foundation. If it does not extend out far enough, that might help explain the shearing inside the Fp. If the masonry had been extended as an elective to get more height rather than damage, you would see a clean break. It also would probably match better. This looks like insurance work.

Bob

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disgusted with some people on this forum. Out of here!