>So what do I do if they have drawn out and capped a queen cell three days after giving them the fresh brood? (It was NOT there when we put it in, we inspected each frame very carefully) Will it even survive?
Most likely. It means they were not far down the road to laying workers and they were still wanting a queen. At that point they will even settle for a drone egg to try to raise a queen, but you gave them what they REALLY wanted (and needed).
> Do I go ahead and introduce a new queen since they decided on their own that they needed one?
If you have a queen, that is one option.
>Do I let whatever is in that cell hatch, or do it cut it off?
If you are introducing a queen, I would remove the cell. If you are going to let them raise a queen, leave it.
> Is it even possible for that cell to actually contain a queen in that situation? I have never heard of this happening.
Is it on the frame of worker eggs you gave them? If so, then it is a legitimate queen.