Does the clear white fluid that is discharged with or without lust count as madhiy (pre-ejaculatory fluid) and necessitate wudhu' (ablution) for prayer, and what are the characteristics of madhiy?

If the discharge is madhy (pre-seminal fluid), then it is impure (najis) and invalidates wudu'. It is obligatory to purify whatever parts of the body and clothing it has touched by sprinkling them with water. Wudu' must be performed for it when one intends to pray. This wudu' is for the sake of prayer, not for purifying the madhy. Wudu' after cleansing oneself from madhy is valid for prayer as long as it is not invalidated by another wudu'-nullifier.