What is the ruling on a marriage that took place without the knowledge of the guardian, and what is the ruling on the child resulting from this marriage?

You are not permitted to appoint your sister's husband or anyone else to conduct your marriage contract as long as your father is alive. Your sister's husband is a mahram and is not allowed to be in seclusion with you. Marriage without a wali (guardian) is invalid according to the majority of scholars, and this is the most correct opinion. As for the child, he is legitimate to the one who marries you due to shubha (resemblance/doubt). We advise you to be dutiful to your father and seek his pleasure.