What is this viscous, shiny, white fluid that comes out after urinating, and must it be washed when purifying oneself for prayer, and are my prayers and fasting acceptable?

The mentioned fluid is likely "wady" (a prostatic secretion). It is sufficient to wash it with water to purify it. It can also be removed by wiping it with a dry cloth three times or more, provided the wiped area is dry. The fast is valid, and the prayer is valid if the impurity was removed sufficiently or if the person was unaware of its presence. It is advised to consult the "Consultations" section of the website for persistent fluid discharge. As for obsessive thoughts (waswas), they should not be given any attention.