What is the ruling regarding a girl's marriage without her family's knowledge, and what is the ruling regarding her child who resulted from this marriage, given the details mentioned?

The couple must repent of what they have done. Their marriage is invalid, for the Prophet, peace and blessings be upon him, said: "Any woman who marries without the permission of her guardian, her marriage is invalid." Performing the marriage a second time without a guardian is not valid unless the officiant is the Muslim ruler or a Sharia judge. The child is attributed to the man due to intercourse under a misconception (waty shubha). The marriage of a pregnant woman due to intercourse under a misconception, where the misconception originated from the man, is valid according to the Shafi'is.