What is the ruling on purifying the private parts from yellow discharge and the small clots accompanying it? Is it obligatory to inspect for them after cleansing with water? And does the ruling on purification differ when sitting on a seat instead of squatting?

One is warned against obsessive thoughts (waswas) and succumbing to them. Yellowish discharge (sufra) and brownish discharge (kudra) are impure (najis), and one must perform istinja' (ritual cleansing) from them. There is no need to search for their presence; it suffices to act upon the default assumption, which is their absence, until certainty of their presence is attained. Then, they should be washed until it is highly probable that they have been removed. In istinja', a strong probability of cleanliness is sufficient. For a woman, istinja' involves washing the external part of the vulva that becomes visible when she squats to relieve herself, not its internal part.