She had a few cuts likely from the force in which I stepped on her. If we try to pick her up she’ll panic and fly off
Right, I understand she may be panicky. Take a light piece of cloth or dishtowel and gently swaddle her in the cloth to capture her wings and lightly cover her head, this will help her calm down. Take care not to squeeze her.
You're going to have to treat her leg and feet, so she's going to have to get used to you handling her. While you have her wrapped and clean the feet and the leg, get someone to take clear photos.
Does the leg and foot have a bad odor???
The hurt foot/leg. It's very hard to tell if it's broken or if it's just badly injured. With the leg becoming discolored, it may be dying due to a break or even infection.
The foot pad has infection or pododermatitis, this is not related to being stepped on, it's been there for a while.
Treat the cut on the leg by cleaning well with chlorhexidine or betadine, then apply triple antibiotic ointment.
As for the foot pad on the injured leg, I would not lance or mess with that very much since it looks like the cut or break to the leg looks bad enough and you don't want to compound the issue further. I'd just clean it well each time you tend to the leg. Hopefully the hardened material will start to soften and you'll eventually be able to work it loose.
As for the other foot, I do agree the nails need to be trimmed. She has a few raised scales and the bottom of the foot from what I can see looks to have some pododermatitis as well. Just soak that foot when you are doing the other one. Apply a bit of ointment to the foot pad and see how it goes. For now, again, I would not attempt to do surgery or remove much material, see if it will eventually come off.
Quail get extremely stressed when handled, they don't seem to be able to take a lot, so I'd provide her with vitamins a couple of days a week to give her a boost.
Not sure how you are housing her, if she's on wire or what, but I'd provide her with either bedding, puppy pads to stand on. Some bedding to snuggle into and perhaps a little box to hide in. They like to hide/hunker down.