What is the ruling on the sensation of drops of urine exiting after showering with hot water, and are the body or clothes considered impure, and what should be done to remove this doubt?

What you are doing—disregarding this doubt and not paying attention to it—is correct. For doubt about the invalidation of purity does not rule that it has been invalidated, and doubt about the emission of impurity is not considered until certainty of its emission is attained. Your non-responsiveness to this doubt closes the door to obsessive whispering (waswasah). So, continue upon this and do not pay attention to these doubts, for they may lead you to waswasah.