Bobwhite and gambels have pretty much the same dietary needs as coturnix and buttons. Here is an article that will help you find what you're looking for. I hesitate to recommend specific brands since you can often find good local brands that have all the nutrition that they need...
That's one of the reasons I'm not fond of AI. In addition to the inaccuracies and making people even less capable of thinking for themselves, the power and resource usage of the immense data centers needed to run it are incredibly resource and power intensive.
Some quail will stay active throughout winter. I have a hen who continues to lay all winter and the occasional crow can be heard. There are always exceptions to the rules.
I don't have a lot of experience with bumblefoot, but I don't see anything that looks like a kernel on those feet. I would keep giving her the warm epsom salt baths and keep her on clean bedding until she heals. You can use antibacterial ointment, but make sure it doesn't contain pain killers.
Your best option would be to send the quail to your state necropsy lab. They will also be able to test for certain diseases.
If you don't want to do that, you can open the bird up and look for physical issues. If you suspect blockage, open up the crop, intestines, etc. to look for one.
That...
Dry hatching can work very well depending on your ambient humidity. You may need to experiment a bit with the settings to find what is ideal for your climate and elevation. For example, I have to add a lot more water to my incubator now that I live in high desert at 4200' above sea level than...
I have never tried giving them raw meat. I don't think they'd eat it. They do love insects, greens and veggies, though. Quail are not as omnivorous as chickens.
When I was in New Zealand a few years ago (okay more like 6 or 7) there were California quail all over the place.
Rats, cats, and stoats will all happily eat quail, so you will definitely want to take that into account.
I would separate her and put her in a warm, dim place for a while and observe her. You will be able to see how much she's eating and drinking, and get a clear picture of what her poop looks like (whether they're all like the one in your pic or whether it's just once in a while).
I do think...
Two years old is getting old for a coturnix quail, so it could be that she's creating less cecal poop than a younger bird would.
I did do a quick search of your previous posts to see what "previously recommended quail feed" was, but didn't find it. What are you feeding her?