Is it permissible for one whose urine does not stop quickly and who experiences frequent madhy (pre-seminal fluid) to perform ablution and pray immediately, given the presence of obsessive doubts concerning the purity of the bag used to prevent urine droplets from reaching one's clothes?

If what you are experiencing is merely a whisper (waswasa), do not pay attention to it, and do not judge that anything has exited unless you have absolute certainty.

If you are certain that urine exits after urinating, and if it stops for a period sufficient for purification and prayer, then wait until it stops, perform istinja (cleansing), make wudu (ablution), and pray.

However, if the discharge of urine is continuous such that it does not stop for a sufficient period for purification and prayer, then you are afflicted with سلس (urinary incontinence). In this case, you must take precautions (tahaffuz), perform wudu after the time for prayer has begun, and pray both obligatory and supererogatory prayers with this wudu until that prayer time ends. According to the Hanbalis, you are not required to repeat the tahaffuz for each prayer time.