Is a woman entitled to marry a righteous man whom her family rejects, knowing that she is not yet married? And does Islam prevent her from marrying herself off?

In Islam, the criteria for competence are religion and character. If someone whose religion and character you approve of proposes to you, then you are permitted to marry him, regardless of his nationality. A condition for the validity of the marriage contract is the presence of a guardian. If your guardians refuse to marry you to someone whose religion and character you approve of, then you may resort to the Sharia courts.