Is there a way to make a “Private Thread Tag” Read only as in nobody can post new posts, yes this might sound strange but we are using a “Private Thread Tag” as an archive and we would like this read only.

Also is there a way to setup moderation on a “Private Thread Tag”

Neither of these are currently available, but thread Archiving is something that is definitely coming with the new forum version - doesn't require making a separate thread tag for it either