As for how long to wait, at least a few days. And you need to catch everyone and give them a dose of Ivermectin. It's just a few drops on the back of the neck, and done. Generally, it's best to do that at night, when everyone is settled into bed.
It depends on how bad the infestation is as to whether it will kill them all. You may need stronger stuff, like permethrin. And if you see dust when you left clean it out, grab the dust mask.
I would catch the hen, bring her in and settle her into a crate/kennel, and then put the chick in with her. And then park right there to pull the baby out if she gets aggressive with it.
I used to use DE a lot, but have recently stopped, as there are studies showing it's very hard on the birds' lungs, which can make them susceptible to lung infections.
Cocci is everywhere. It isn't something you can clean away, unless you keep your birds away from dirt their whole lives, and keep any dirt from your shoes out of the coop.
If it's Coccidosis, the Corid will cure it in the birds, and let them get their immunity up. But if they got it because the...
The mites you mentioned need treated (I'd do it with Ivermectin, myself), and the coop treated with a dusting. They can bleed a bird to death easily enough. I don't know if that was what killed the babies or not, but it certainly could have.
As for the spots of blood, the only thing I can...