Is a young man's kissing and embracing a woman considered zina (unlawful sexual intercourse) that necessitates a hadd punishment, if a "paper marriage" that was not publicly announced, but witnessed by two Muslims, had taken place between them, while the young man believes this marriage to be permissible on the grounds of the witnesses' presence?

For a marriage to be valid, the woman's guardian (wali) must be present, based on the Prophet's (peace be upon him) saying: "Any woman who marries without the permission of her guardian, her marriage is invalid." What transpired between you two is not a legitimate marriage due to the absence of the guardian and his consent. The document written by the lawyer holds no value if it was done in your absence. This man is not your husband, so it is not permissible for you to allow him access to yourself. We advise you to rectify this marriage and declare it as a valid, legitimate marriage, out of concern for your chastity and virtue. Either a valid marriage, or a complete separation from him.