Is the body considered impure, necessitating re-bathing if a speck of feces is found under the nails after bathing? And are the clothes and furnishings used for prayer considered impure in this case?

What the questioner mentions are mere whisperings (waswas), as evidenced by her statement: "knowing that after relieving myself, I wash my hands thoroughly with water and soap." It is customary that whoever washes their hands thoroughly with water and soap will not have any trace of impurity remaining on their hands. We advise her to ignore these whisperings and turn away from them. The default state of things is purity, and this default is maintained until proven otherwise with certainty. Consequently, the water she bathes with is pure, as are her clothes, prayer mat, blanket, and other items. Their purity is presumed until their impurity is established with certainty. Mere doubt does not form the basis for any ruling.