After cleaning can you see better how much beak she has left? If the entire beak is missing, I don't think they grow back, but if some of it is still there, it can grow back, but I'm not sure at what point the beak
wouldn't grow back. There have been instances of 3D printing beaks but I think that's a bit beyond the skill of most people.
Here's info on chickens regrowing beaks with exposed tissue and how to treat it and feed them:
https://the-chicken-chick.com/repairing-chickens-broken-beak/
If you think the beak can be regrown (I really couldn't see in the pic what was going on, poor thing), then keep using your little box sling for her leg.
If there isn't much left of the beak though, and you're not comfortable tube feeding her if she can't eat, I agree with others that putting her down is best. Cervical dislocation is the most humane method and there are youtube videos for this. I myself was uncomfortable with this for fear of making a mistake, so I'd probably use the chopping block because it's the next fastest way and over quickly.
I don't envy your position. This is the inevitable in chicken keeping. We come to love them dearly, but so do all of the predators. My heart breaks for you because I've been in your shoes. You are doing the best you can for your sweet hen. I hope your parents are willing to lend a hand.