What is the ruling on the marriage of a girl who fled her father's home and lived with a young man, and the young man's family married them off without the father's permission or consent, and she is now pregnant without her father's knowledge?

It is not permissible for a girl to run away from her father's house. This is a forbidden act that necessitates immediate repentance. Marriage without a guardian (wali) is invalid according to the majority of scholars. If such a marriage occurs, it takes on some rulings of a valid marriage, such as the attribution of lineage, and it can be validated by a decision from the Sharia court or by the guardian's endorsement.