How can one get rid of purity-related obsessive thoughts, and what is the correct lawful method of ritual bathing to overcome these obsessive thoughts that affect one's psyche and cause delays in prayer?

The cure for obsessive whispers (waswas) is to ignore them and pay them no heed. If it is highly probable that water has reached all parts of the body after the intention to remove ritual impurity or permit prayer, then the purification is valid. Saying "Bismillah" before ablution and ghusl, and supplicating afterwards, are Sunnah and their omission does not invalidate the purification. It is not obligatory to perform ghusl after sleeping on a ritually impure mattress; rather, only the area touched by the impurity should be washed if one of the two bodies was wet. Ghusl is not obligatory for past masturbation unless the emission of semen is confirmed, and one ghusl is sufficient to remove all previous ritual impurities. There is a difference of opinion regarding making up prayers performed without purification. If Hajj was performed with doubt about purification, the original presumption is its validity. However, if Tawaf was definitely performed while in a state of major ritual impurity (janabah), then you owe a camel (badanah) or fasting for ten days.