Not really. Only if an infestation is really, really bad can they be seen on the outside of a hen or crawling around the coop. Best chance is to grab one or two off the roost at night and then check carefully around their vent. If they are mites, you should be able to see tiny, moving black...
Were they with a rooster in their previous flock? Sometimes a rooster can cause bare bottoms. I would also check for mites if you haven't already done so.
I have one pullet who just loves to dig in the nest boxes like your hen in the video. I keep hoping she's going into to lay an egg, but no, it's just to kick all the straw out searching for things to peck.
It looked like there were also some bright red drops of blood of the wood near the nest box. That's what made me think that there may be a more conventional wound involved.
Are you sure the blood is from egg-laying? I've had some poor hens lay huge double yokers and have never seen blood like that.
Just speculating for a minute -- This is a new environment for these hens and perhaps there could be some squabbling and pecking as the re-establish their pecking...
None of my chickens like to be held or touched, but then again I've never really worked at it. I sometime wish I had, it would make it easier to pick them up when I need to examine them.
My poor chickens. Leftover meat never makes it past my dogs. They have to content themselves with mealworms and whatever snails I can find to pitch into their yard.
If Aart and lazy gardener think they can be immediately integrated, than I would try that, rather then the 2 day separation I suggested. It's much simpler that way and it does seem doubtful that your rooster would be aggressive to incoming hens, or that the hens would be aggressive to a full...
I've been following the story, and am so, so, sorry for what you went through. Just wanted to say that I'm glad your rooster is pulling through and that you are getting him some companions. I would probably start by putting some kind of divider in your coop and/or run where the new hens can...