What is the transparent, viscous fluid that is discharged after urination when thinking about or looking at intercourse, and how does one purify oneself from it, given the frequent doubt regarding prayer and ablution?

The fluid that exits after looking at or thinking about intercourse is 'madhy' (pre-seminal fluid). It is impure (najis) and invalidates ablution (wudu').

Regarding excessive doubt in ablution and prayer, one must discard the doubt and pay no attention to it, turn away from whisperings (waswas), and complete the prayer without performing the prostrations of forgetfulness (sujud al-sahw). This is because when excessive doubt becomes a form of waswas, it becomes obligatory to disregard it.