Harman TL 300 Problems

Although it doesn't look exactly like my stove, the larger metal piece looks like it could be part of the damper frame. You said that warped piece right under the bypass was ceramic, but isn't it metal? It looks like the lower part of the damper frame is itself warped --- which would explain why there is a big gap that allows you to look through to above the combustion chamber (at least that seems to be what the picture shows, but I'm not positive).

You should be able to reach up and feel around the damper, where it closes to meet the frame, to see if the frame is intact the whole way around - on my stove it has two bolts just above the brick face (with two metal spacer to hold the bricks) and two bolts at the center top, where the damper meets the frame when the damper is closed. But if that warped piece is ceramic fiberboard, and not metal, then the picture seems to show you have no damper frame at all - I really can't tell from the one pic.

What is your usual stovetop temp when you run the stove?

Does the bypass damper still work?
Almost looks like the crack in picture 3 was allowing air into the unit which could cause damage to the bypass area.

For the pieces in picture 1, the 2 smaller pieces almost look like your andiron extensions.
I had a similar problem with mine, my dealer replaced them under warrantee.

https://www.hearth.com/talk/threads/tl-300-andiron-and-andiron-extension.64127/

Just guessing but your stove looks like it has been run in an overheat condition for some time. Possibly due to air getting into places where it should not be entering for some reason. What air setting do you normally use. My stove is always on low,perhaps thats why it still looks new inside and out after 5 years.

My damper etc looks the same. My damper rod falls passed damper and that causes damper to not close tight. What did your dealer say.

In the photo it looks like the damper was left open too long and the stove overheated. That can happen to an unattended stove on warm up. Mine almost got away on me once but i caught it in time and its fine,so now i dont leave it unattended on warm up. Now there is no seal around the damper door at all anymore and the stove will destroy itself if run that way and not fixed. I doubt warranty will cover that,clearly an overfire issue.