Is the money spent on a female student not considered her rightful due, given that she does not assist the doctor, and must she ask the doctor to assign her tasks to perform?

If the university requires the assistance of one of the professors to disburse funds, and you offered your help to the professor, who then excused you from it so you could dedicate yourself to your research, and if this exemption is within his authority, then you have done what is required of you and are entitled to the funds.