How is clothing purified from pre-seminal fluid (madhy), is there a difference between pre-seminal fluid (madhy) and vaginal discharge, and is one sinful for not caring about that in order to ward off obsessive doubts (waswasa)?

You are afflicted with waswasah (obsessive whispering), and its cure is to ignore it and not pay attention to it.

The original state is that purity remains unless there is a certain nullifier. So, if you doubt that something has exited, do not pay attention to the doubt, based on the Prophet's (peace and blessings be upon him) saying: "If any of you finds something in his stomach and is unsure whether something has exited from him or not, he should not leave the mosque until he hears a sound or perceives a smell."

If you are certain that something has exited, then if it is madhy (pre-seminal fluid), it must be purified and sprinkled with water once. If it is from vaginal secretions, it does not require purification; rather, ablution (wudu') is required for prayer, as vaginal secretions are pure.

The desire that necessitates the exit of madhy is that which usually occurs with thoughts of intercourse and the like. As for mere fleeting thoughts or hearing a sound, madhy does not exit due to them. You are not required to inspect or search to see if anything has exited or not. If you doubt its exit, do not pay attention to the doubt.

If you see something and are unsure whether it is madhy or from vaginal secretions, you may choose and assign it the ruling you wish.

You are not sinful for disregarding these waswasah; rather, this is your legal ruling.