I picked up the nuc on April 9th, so I've had it now for about 5 weeks.
If you have had it for 5 weeks, then there was a laying queen in there a couple weeks ago for sure, reference all the capped brood.
Cant say for sure about some things as I'm not clear, is the amount of bees on those frames what they were when you pulled it up, or, is it after you shook some off ? The frames do not look like a lot of bees, looks more like an absolute minimum number of bees for those frames.
Gong thru the photos. Number one, some capped and what looks to be a lot of emerged around that, with a honey border. Check in the uncapped cells there, that's where I would expect to find eggs and lavae. Photo 2. That's a nice frame of capped brood. Photo 4, agree with otheres, looks like they have a start on some wonky comb there, you dont want that to continue. It's very important when dealing with undrawn frames to make sure they are pushed together tightly, otherwise wonky comb like that shows up all to often.
Photo 3 is the interesting one for me. The frame itself is a mix of capped drone, worker, pollen and honey cells. My experience over time, once a frame gets like that with pollen intermixed between brood the way that one is, they never fix it, and I try cycle them out over time.
I downloaded the photo to take a closer look, would be very helpful to have a higher resolution copy, this one is fairly low resolution and appears slightly blurry when you blow it up. On the far right side, about 1/3 of the way down the frame appears to be a queen. It's not quite clear enough to be positive, but I believe you have a queen in that photo. The thorax looks like a queen, but the abdomen doesn't appear to be as long as the wings. Might be a queen with her butt stuck into a cell trying to lay an egg, or, it could be a virgin queen, and I'm hedging to say it's a young virgin queen.
So based on limited knowledge, my thoughts are that this colony has swarmed, based on the low population and presence of what appears to be a virgin queen. Population will explode when that frame of capped brood emerges, and that's when the bees will finally start to get serious about building some comb.
Agree with others, get the second box off until you have bees on 8 drawn frames if it's a 10 frame box.