What is the ruling on praying at home, and what should someone afflicted with waswas (obsessive doubts) do concerning the purification of madhy (pre-seminal fluid) scattered on furniture, and water splattered from istinja' (cleaning oneself after urinating/defecating) onto the body and faucet, and the small, hard-to-remove spot on the toilet seat?

Waswasah (obsessive whispering/doubts) is a serious disease whose cure lies in ignoring it. Do not judge your body or clothes to be impure unless you have certainty that you can swear by.

If the impurity is madhy (pre-seminal fluid), then sprinkle water on the garment and wash whatever touched the body. As for the impurity of urine, what you perceive as water splashing is often an illusion and waswasah, so do not pay attention to it.

If you are certain that urine has touched your body, it is sufficient to pour water over the affected area; there is no need to scrub it.

What you imagine to be impure on the floor and furnishings is waswasah, so do not pay attention to it. Even if something were to become impure, impurity does not transfer to a clean, moist, or wet surface according to many scholars. It is permissible for someone afflicted with waswasah to take the easiest of scholarly opinions.