First of all THANK YOU for taking this girl in and looking out for her (and your English is just fine by the way), I teared up when I saw that picture.
I agree with Robin and Deborah, this is much like when you have people recovering from starvation situations, if you suddenly flood the system with nutrients it can be enough of a shock to finish them off. Just take it slowly and gently.
Since she's drinking on her own, you probably do not need to worry about pedialyte and I would definitely stay away from injections (just more stress). I have had success with it in the past, but it's usually reserved for severe dehyrdation, which she doesn't have if you've seen her drinking. Just let her do her thing.
It sounds like she's a fighter, I'm amazed she's survived in that condition, let alone is still moving around her cage. I hope she keeps fighting for you, and we would love continued updates on her progress. Best wishes for you both.