بسم الله الرحمن الرحيم
(1) Yes, your parents may offer nafl qurbani in their parents’ name by this money as well as give it in charity.
(2) If she coughs so much that she cannot offer salah of one time by making wudhu in the state of taharah then she is mazur. She should make wudhu for the time of each salah and offer salah in the same condition. Her salah shall be valid though the drops of urine keep on coming. If it is not so then she will have to offer salah again in case of urine drops. You should get her treated by any expert Unani physician, her coughing problem shall go away.
Allah knows Best!
Darul Uloom Deoband