I would agree with the camera inspection. If you are having mortar fall
down and have been taking in water for some time...it could be real
ugly in that chimney and you need to know how bad the chimney is
damaged, especially since you are using this fireplace.
Im not a real fan of chimney top dampers. when they are closed heated
air raises up and then cools and sinks down again. It casues a cold
draft feel at the hearth even if there is no outside air getting past
the damper.
A good combo is a stainless chimney cap (none of that galvanized
garbage at home depo) and a chimney balloon to get a tight seal down by
the firebox.