As a new beekeeper of only a year I am sure someone will correct me but if the bees have destroyed the QC you put in there it sounds like you have a Queen. Could she be a virgin Queen which hasn't started laying. If so she can take a good long time to start laying.
The hive was a swarm that seem to split on the next day where part of the swarm went away and the other bit stayed behind. So that is a swarm that swarmed again spliting itself again. This swarm came from one of my hives so it did have a queen.