What is the ruling regarding the white spots a young man finds on his underwear, even though he does not feel them being discharged? And is what he does, placing a piece of cloth over his private parts and changing it for every prayer, permissible?

Refrain from inspecting and searching for anything that might exit your body, as this leads to waswas (obsessive whispers). Do not rule that anything has exited unless you have certain, firm conviction upon which you can swear. The default is that nothing has exited. If you are certain that something has exited from the front (penis), then anything that exits from the opening of the penis is impure and necessitates istinja' (cleansing) and wudu' (ablution) for prayer. If you are certain that it is madhiy (pre-seminal fluid), then purify yourself from it as explained in Fatwa No. 59304. If you doubt whether it is madhiy or something else, choose and assign to it the ruling you wish (Fatwa No. 68364). What exits after urinating is wadiy (thick white fluid that exits after urine), and its rulings are in Fatwa No. 100078. If the discharge exits continuously such that you do not find a period of cessation, then your ruling is that of one afflicted with sils (incontinence): perform wudu' for prayer after its time has begun and pray as much as you wish (Fatwa No. 97134). Most likely, these are merely waswas, so you must disregard them.