Is it obligatory to perform ablution (wudu') and wash the penis and testicles when a small, dry or moist drop of madhiy (pre-ejaculatory fluid) exits some time after urination, and what is the ruling on repeating this for every prayer?

Al-madhi (pre-seminal fluid) is impure (najis) and invalidates wudu'. It is sufficient to wash the spot where the madhi touched, and it is not obligatory to wash the entire penis or the testicles. There is no need to designate a special garment for prayer; it is enough to sprinkle water on the garment that was affected by the madhi. If you are uncertain about the emission of madhi, it is not necessary to wash its spot, as the default is that it has not exited until certainty is achieved.