What is the ruling regarding water droplets that descend after urination, are they impure, and what is their effect on the validity of prayer and fasting?

The emission of urine drops nullifies ablution, and it is originally impure. If these drops cease and stop flowing, allowing you sufficient time to perform the prayer, then you should wait for them to stop, then perform ablution and pray. However, if they are emitted most of the time, such that you do not find sufficient time after their cessation to perform the prayer, then you are considered to have chronic incontinence (sahib al-salas). Purity is not a condition for fasting, so its absence does not affect the validity of the fast.