Engine issues

What do you mean by "dropped the valve seat", because I did not read that these valve seats are inserts or anything like that.
It seems to me as though whomever sold the cylinder head would be responsible for the warranty but I doubt if they are going to assume responsibility for the labor as well or even if the entire engine if that is the fact.
If a valve on number seven actually came loose because of the keeper not properly installed, then maybe the shop doing to the labor could be held accountable.
I assume you have already disassembled the engine or had someone do it, so you should be able to tell what happened. Can you or did you already take it apart or have all you done so far is the compression test?

It has been completely taken apart at the dealership and ran all necessary tests. The head gaskets and cylinder heads were replaced. I read that they replace all of that included. The repair shop that did the work warranties parts and labor.

What do you mean by "dropped the vale seat"?
Or was that just something you were told?

That is what I was told. It went down into my engine because my engine overheated and completely ruined my engine. I saw that if your valve seat is going through your car will run really rough which it was. What test would they do to determine that before my engine was completely gone? I am trying to determine if the repair shop did everything they could have to to prevented the damage done.

Valve seats that I know of do not just drop out. They are machined into the cylinder head. If in fact the valve dropped out, perhaps that is what they told you. That could happen if the valve keepers were not installed correctly and rechecked afterwards. I usually bang on the tops of the valves with a rubber hammer after installing the keepers to make sure they seat.
Have they explained to you what happened exactly without using ambiguous language?
This diagram shows how the two halves of the valve stem keepers look like, #1.