Is it permissible for a widow to marry without a guardian, and what is the ruling on her marrying secretly, and what are the the conditions for a widow's marriage if her family is alive?

The widow and others are equal in the requirement of a guardian (wali) for the marriage contract; there is no difference between them except in seeking permission. This is indicated by the Prophet's (peace and blessings be upon him) saying: "There is no marriage except with a guardian," and his saying: "Any woman who marries without the permission of her guardian, her marriage is invalid, invalid, invalid. If he has intercourse with her, she is entitled to the dower for what he made lawful of her private parts. If they dispute, then the ruler is the guardian of the one who has no guardian."

If a woman marries without a guardian, her marriage is invalid, and she must separate from her husband. If her parents are alive, her father is her guardian. If he is not present, then her sons, if they are mature and adult. Otherwise, her brothers, then the rest of her 'asaba (male agnates).