What is the ruling on the feces or egg of a sewer cockroach, are the measures taken concerning it correct, and what are the implications of it touching hands, clothes, shoes, and praying with them?

The cure for the waswas (whispers/obsessive thoughts) you are experiencing is to ignore them and pay no attention to them. As for cockroaches in toilets, scholars have differed regarding their purity. Even if we assume they are impure, whatever touches your hand from their waste or eggs remains pure, because the default state of things is purity, and this state is only superseded by certainty. Therefore, your hand and your shoe have not become impure, everything your hand has touched is pure, and all your prayers are valid with those clothes, and you are not required to repeat them.