How do I purify myself from madhy (pre-seminal fluid) that exits intermittently? Do I have to wait for fifteen minutes, for example, until its emission stops, then perform ablution (wudu') and pray?

Pre-seminal fluid (madhy) nullifies ablution (wudu’). It is impure (najis), and one must ensure its complete cessation by being certain that its discharge has stopped; there is no need to wait for a specific period. It is sufficient to wash the affected area of the body to purify it, and it is sufficient to sprinkle water on the garment that it has stained.