What is the legal ruling regarding recurrent doubt about the emission of madhy while thinking about men, and must ablution be repeated for every prayer?

You must cast away obsessions (waswas) in acts of worship, for religion is ease, and Allah is merciful to His servants, and He does not burden a soul beyond its capacity. Indulging in obsessions corrupts one's religion and worldly life, and it causes one to miss the virtue of praying on time, and perhaps even to miss the prayer's prescribed time. This is a great entry point for Satan.

The cure: 1. Seek refuge (in Allah) and turn away from the obsession. 2. Do not repeat ritual cleansing (istinja') after having a strong presumption of cleanliness. 3. Do not exceed washing the limbs during ablution (wudu') more than three times. 4. If Satan whispers to you that you have not washed a limb or that water has not reached it, say with your state of being: "Yes, I have washed it, and the water has reached it." 5. Seek refuge (in Allah) and cease the obsession, and respond to Satan's whispers with certainty in the correctness of your worship, so that Satan may be driven away from you.

The difference between madhi (pre-seminal fluid) and mani (seminal fluid): Madhi: A thin, white fluid that is discharged upon thinking about or engaging in foreplay. It is not followed by fatigue in the body. It necessitates cleansing the affected area and performing ablution (wudu'). Mani: For women, it is a thin, yellowish fluid, its scent resembling that of a man's semen. It necessitates a ritual bath (ghusl). If you doubt whether something has been discharged, base your decision on the original state, which is that nothing has been discharged, and do not investigate. Normal vaginal discharge (vaginal moisture): It is pure (tahir) but necessitates ablution (wudu'). If you are in doubt between mani and madhi, choose between them; this is easier for one afflicted by obsession. If you perform ablution and then vaginal discharge appears, you must repeat the ablution because it nullifies it.