What are the rulings regarding purity (tahara) and prayer (salat) for someone who suffers from temporary urinary incontinence ( سلس البول المؤقت) and whose dripping (تنقيط) continues for approximately two hours? Is it permissible for him to pray during this period?

If you do not find enough time to perform the prayer with proper purification, then you are considered to have سلس (incontinence), and you perform ablution after the prayer time begins and pray as much as you wish. However, if you find enough time, you wait until that time arrives to perform ablution and pray. If the situation differs between prayers, then each prayer has its own ruling: if you know that the incontinence will not stop before the time expires, then perform ablution and pray. But if you know that it will stop, then wait, perform ablution, and pray.