Well, now I'm really showing my ignorance! Unlined? I don't know. How do I find out? The house was built in 1978, if that's any help at all.
The loose brick in in the center back of the fireplace, approximately two feet from the fireplace floor. And, yes, we do burn wood in the fireplace during the winter months. There is a damper which is kept closed when the fireplace is not in use.
A rain cap? There are two metal, cage-like structures on top of the chimney. We had them installed because we had a problem with birds entering our ductwork in the basement.
Is there such a thing as a chimney fire that we should be concerned about?