What is the ruling regarding my past prayers that I performed immediately after drops of urine were discharged, without waiting for them to stop, and am I required to make them up, and how should I make them up?

If you are certain that drops of urine have descended, then you must wait until they stop, then perform istinja' (washing of private parts) and wash the impurity from your clothes, then perform wudu' (ablution) and pray. The Malikis consider such impurity excused. As for the prayers you performed without purity while you were certain that urine was exiting, you must repeat them according to the majority of scholars. However, according to Ibn Taymiyyah, repeating them is not obligatory due to ignorance, and it is permissible to act upon Ibn Taymiyyah's opinion to remove hardship. But if the exiting of these drops is merely a doubt, then the اصل (presumption) is that nothing has exited, and your prayers are valid, and there is no need to repeat them.