What is the ruling on the prayer of someone who suffers from drops of urine exiting after urinating? And is he required to purify his clothes every time, or is it permissible for him to wait for them to stop, then perform ablution and pray? And is it permissible for him to pray with the ablution of Dhuhr if he is certain that it will not be invalidated until the Asr prayer?

You are not afflicted with سلس (incontinence), so you are not required to perform ablution for every prayer. Rather, you can pray as many obligatory and supererogatory prayers as you wish with your ablution until your ablution is invalidated. You must take precautions by placing a cloth or tissue and waiting until the dripping stops. Then, you clean yourself (istinja') and perform ablution (wudu') and pray. It is more prudent to remove the impurity unless it is extremely difficult for you to do so, in which case you may adopt the view of the Malikis that its removal is not obligatory.