Does the excretion of one or two drops of urine after resisting the urge to urinate necessitate changing clothes or invalidate the prayer, and is the water that falls when washing the penis after urinating impure?

The emission of one or two drops of urine invalidates ablution (wudu') and necessitates washing the defiled area only. It does not necessitate a full ritual bath (ghusl) or changing clothes. The default state of a place is purity unless the emission of something is certain. One should disregard obsessive thoughts in this regard. As for the water that drips during istinja' (washing after relieving oneself), it is pure unless it changes due to impurity.