Does the scarcity of menstrual blood (a few drops) due to health issues render a girl in the state of ritual purity, and is it permissible for her to perform ghusl, prayer, and fasting, and does she have to make up the days after Ramadan?

These drops of blood are considered menses according to the Maliki school, so you must perform ghusl after their cessation, pray, and make up the fast for the day you saw the blood. As for the majority of scholars, they do not consider it menses, and what you are doing is in accordance with the view of the majority of scholars.