What is the ruling on the prayer of one who finds a urine-like smell in his underwear, with no visible impurity present, and are his past prayers valid? And is his prayer permissible if yellow stains remain in the underwear after washing it?

If you are afflicted with waswasah (obsessive whispering), pay no attention to it. However, if you are not afflicted by it and you are certain, with definitive conviction, that urine has exited due to the presence of its trace, then your wudu' is invalidated, and you must perform istinja' (washing the private parts) and wash the area of the urine on your clothes. If you doubt the time of its exit, attribute it to the closest probable time. As for doubt, nothing is required of you, because the default assumption is that nothing has exited. The spots on the trousers might be from sweat. If you prayed while being certain that urine had exited, then your prayer is not valid and must be made up.