What should one do who notices traces of urine on his underwear after prayer, and feels drops of urine descending during prayer despite his attempts to completely empty his bladder? And is it permissible for him to place paper tissues in his underwear to prevent urine from reaching it?

If the emission of urine drops is continuous and does not stop for a time sufficient to perform prayer with proper purification, or if it sometimes stops and sometimes not, then your ruling is that of a person afflicted with سلس (incontinence). You should perform ablution for each prayer after its time has begun, take precautions, and pray. What is emitted will not harm you. However, if it stops for a known period that is sufficient for purification and prayer, then you must wait for that time, purify yourself, and pray. If urine is emitted during the prayer, it becomes nullified, and purification and prayer must be repeated.