My guess it is will grow back but it just depends on how much of the quick was damaged. We’ll have to wait and see.
It will probably bleed whenever the soft tissue gets bumped. That sounds typical of a toenail removal. I remember that happened pretty frequently when my Peppy lost her toenail. Eventually a thick enough scab or new keratin will cover the exposed vessels enough so that it doesnt bleed as much. It will probably take weeks to grow a nail back, but I would think probably within a week or so it will stop bleeding when bumped.
I do wonder if she had the whole toe tip damaged somehow. It looks pretty munched up, but it could just be the picture. If she were mine I would probably try to apply an ointment once a day, but it could be a moot point since she uses her toes to dig around even damaged. Could help protect the toe from bleeding as much, too. I think you said you’re using a blam of some sort, so that would function the same as an ointment to hep protect the exposed tissue.
I don’t think it’s a balance issue, but I would think it’s very sore based on how it looks. I am wondering if there is bruising around the toe tip, but hard to tell from pics and with her scale color. I know when I cut a nail too short or have even a hangnail, sometimes my whole finger is out of commission and I don’t want to use it bc bumping it is painful; i would be that’s how she feels about her toe. Do keep an eye out for infection, but like people, some chickens probably have a bit lower pain tolerance. I know we have a drama queen in our flock. I hope she feels better soon. Daily improvements are good.