Is my prayer valid if I doubted the pronunciation of the Taslim (salutation of peace) and repeated it while facing right, and is it permissible for me to pray while sometimes experiencing urine leakage, knowing that I suffer from obsessive doubts regarding purity and prayer?

It is clear that obsessive whisperings (waswasah) have taken a toll on you. You must cast them away, ignore them, and completely disregard them. Your prayer is not invalidated by repeating the taslim, because exiting the prayer occurred with the first taslim. If the spotting is merely a doubt, do not pay attention to it. However, if you are certain of it, then your ablution is nullified and your prayer is invalid, and you must repeat it with a proper state of purity, while waiting for the cessation of the discharge, as long as you are not afflicted with incontinence.