Welcome, Ece and baby gray (what's his/her name?). You have a VERY young baby in your hands. In the wild, it would not have come out of the nest yet so you need to supplement her food with handfeeding as well as offer two different kinds of soft food served warm and fresh twice a day. Please make sure she is kept in a safe environment (perches low to the bottom of the cage, something soft on the bottom in case she/he falls, safe bar separation so he/she doesn't get a foot or head stuck in between them, etc) and don't even think of training until she is a juvenile because, even though it will work right now, it will backfire on you if you do it. Baby parrots are like human babies, all they need is warmth (make sure he/she is kept VERY warm), softness, good nutritional food and lots and lots of love - human babies don't go to school and baby parrots don't get training until they are older.
Has he/she had an ionized calcium test to determine if his/her calcium levels are normal? Because the fact that he/she had a broken leg in the nest worries me as this is usually caused by a calcium deficiency.