How authentic are the hadiths mentioned in the Sunni Sahih collections regarding temporary marriage (nikah al-mut'ah), and is it possible that two Arabs would ask the Prophet for castration?

Mut'ah marriage was permitted then forbidden, and this is established in the authentic Sunnah, not interpolated. As for castration, it was known among the Companions, and their asking for permission regarding it is proof of that. One must be wary of boldness in religious matters and speaking without knowledge. Whoever finds a matter unclear should ask the people of knowledge, because lying about Allah and His Messenger is among the greatest major sins.