What is the ruling on continuous doubt about the emission of prostatic fluid (madhy) after urinating or seeing girls, and what is the ruling on prolonging ablution (wudu') for fear of its invalidation? And is the fast of one from whom madhy was emitted, and who did not perform ghusl, void?

Doubt about the emission of madhy (pre-seminal fluid) should be disregarded. The default assumption is that it has not been emitted, and certainty is not overruled by doubt. The emission of madhy due to looking does not invalidate the fast according to the majority of jurists. In this case, one should wash the male organ and perform wudu (ablution). Similarly, wady (a thick, white discharge that may appear after urination) does not invalidate the fast; one should wash whatever it has soiled and perform wudu. What the questioner is experiencing, namely an exaggeration in wudu and doubt concerning it, is obsessive-compulsive disorder (waswas al-qahri). Its cure lies in ignoring it and reciting the Mu'awwidhatayn (Surahs Al-Falaq and An-Nas). Washing a limb more than three times is an act of transgression and extremism. Whoever fasts but does not perform some of the prayers has committed a grave sin and must repent and make up the missed prayers. However, their fast remains valid.