Just butcher the male, if you are willing to keep the two females for a little longer. Butchering is as easy as culling, quails being one of thee easiest to butcher. I say that you either butcher them all or butcher the male and keep the two females. Don't keep the three together, the females...
If the Jersey Giant is your dad and the chick has barring, then the mom has to be the BR. Which also means that your chick that has barring is a male. You unintentionally created a sexlink.
DE is safe for the coop, but I wouldn't use it. It works horribly and is bad to breathe in. For scaly leg mites, I recommend coating their legs with a thick coat of vaseline. Works like a charm, but I definitely recommend using gloves when doing it.
To answer your first question, that is correct. To answer your second question, you would get a mutt. Not a red sexlink, the sexlinkage doesn't carry on. If you want a black sexlink, consider crossing your BCM with any barred hen. Cuckoo Marans are a popular choice when creating black sexlinks...
I see more than 2 EEs and several red sexlinks. EEs can't be a full EE. Not sure what you meant on that. At least where I am from, EE stands for Easter Egger. Nice pheasants.
When someone walks across the garden and doesn't stay on the path. This is mostly because they stomp all over the plants, and who likes that? I hate it when people pretend to know a lot, but actually know very little. And I dislike it when people say "no offense" and proceed to offend someone...