What is the ruling on the prayers performed by someone who continuously finds traces of faeces in their underwear after using water for purification, and what should be done about it?

If the questioner ignores the effect of feces after noticing it and goes to pray, and does not repeat past prayers but purifies himself for the present prayer, that is correct if he is not certain that it exited before or during the past prayer, because the emission of an impurity after prayer does not affect its validity. And if he doubts the time of its exit, the impurity is attributed to the nearest time and considered to have exited after the prayer.

However, if he sees the effect of feces and then ignores washing it, and prays while still contaminated by it, his prayer is invalid, and he must repeat the prayers he performed while knowingly contaminated by the impurity.

What is required in istinja' with water is to remove the substance of the impurity and its traces until the roughness of the area returns to what it was, and a strong presumption is sufficient for that.