What is the ruling on a father killing his son who caused his daughter to become pregnant through fornication, and what should he do with his wife who concealed the matter, and is it forbidden for him to place the grandchild resulting from this relationship in an orphanage?

What happened with your daughter was due to negligence and laxity on your part and her mother's. You are not permitted to kill the young man, as it is a sin, and the ruling for a killer is to be killed in retribution (qisas). The marriage is invalid if it was without a guardian (wali) and witnesses, by agreement of the imams. It is considered a "secret marriage" (nikah sirr), resembling the marriage of prostitutes, and must be annulled. If the young man believed the marriage was valid, then cohabitation is considered "intercourse by way of شبهة" (intercourse under misconception), and the child's lineage is established with him. The child should be left with his mother, and his expenses are the father's responsibility. If the marriage had witnesses but lacked a guardian, it is invalid according to the majority of scholars, but the child's lineage is established with his father. Your wife sinned by concealing the young man and betraying trust, but we do not advise you to divorce her due to her interpretation (of the situation) and her fear for you.