Re: Please help diagnose what this is... Video..
Your nucs adult bee population appears to be very weak, I don't know if the brood has died from neglect or from varroa mites, or both. I would say that the nuc came from a colony that had a large varroa mite/virus population. If the adults can't cover all of the brood area, I would recommend reducing the number of frames down to what they can cover. If any other colonies that you may have can spare a frame or 2 of nurse bees, that would help, if the problem is lack of care.
The uncapped brood I can see looks gray in the video, are they pearly white when you are looking at them during your inspection? If they are gray they could have been chilled due to the lack of adults needed to warm the brood areas. Do you see any dead larvae that have died before being capped?
If you can't see inside the queen cell use the hive tool to spread the mouth, the bees will redo the entrance with no problem. It is common for the bees to build queen cups in the spring, it is only a problem when the are occupied by an egg or larva.
37 years - 25 colonies - IPM disciple - naturally skeptic