Dislocated metal plate in Thunderbolt port
I had this problem fixed by Apple. Phone support claimed they could only help me with software problems. I didn't try to get through to the Customer Relations. Instead I tried visiting another Apple Store, where they were happy to fix the problem within warranty. This is a costly repair to pay yourself, as the whole "logic board" has to be replaced.

Regarding my specific questions:



  Does anyone know what is the functionality of the dislocated piece? I googled for the specifics of the connector, but couldn't find any documentation.


In my best understanding, the dislocated piece is only used to hold the connector in place. The only other use I can think of is for grounding. However, thunderbolt connectors already have a ground pin. So if you are out of warranty, before shelling around $600 for a repair, you may want to try cutting the metal pin and see how it works for you.

  I have an AppleCare Protection plan. Shouldn't this be covered by AppleCare?


Well, it depends on whom you ask. In the first Apple Store, the Genius was adamant that the problem was caused by misuse so it was not covered. In the second Apple Store the Genius directly recognized it as an assembly fault and fixed it for free. So, don't be discouraged by a first rejection of your claim. Try again, different time, different place (if possible).

  Are there any other avenues to pursue a repair from Apple? 


If you don't manage to get a repair from an Apple Store, trying to get through to Customer Relations as suggested in the comments above may be an option. Another option would be to try having the problem fixed by an Apple Authorized Service Provider, who may have a less judgmental attitude.