Use your entrance reducer to help control robbing. It want matter about the size of the cells on the brood from the other hive. You can take care of that later. Nor will the emerging time of the brood. Just pick a frame with mostly capped brood.
If you found an unmarked queen I would leave her. It is not uncommon for a package to supercede. She may not be laying yet. Give them two frames of brood, one now and another in 10 to 12 days. That should give enough time to see what the new unmarked queen is going to do. Thats what I'd do.