Is a girl considered a wife شرعًا (Islamically) and must she be divorced, and what is the extent of the validity of her breaking off the engagement, and is it permissible for someone other than the first fiancé to propose to her as long as he has not broken off the engagement?

The madhhab of the Shafi'is and the majority of the Hanbalis is that marriage (nikah) is not contracted except with the word "nikah" (marriage) or "tazweej" (giving in marriage). According to the Malikis, it is contracted with these two words, and also with the word "hibah" (gift) when a dowry (sadaq) is mentioned. As for the Hanafis, they hold that marriage is contracted with the word "tamleek" (transfer of ownership) and with every word that indicates an immediate transfer of ownership of the object.

The most preponderant opinion is that of the majority, based on the saying of the Prophet, peace and blessings be upon him: "For you have taken them by the trust of Allah, and made their private parts lawful to you by the word of Allah." And the "word of Allah" here refers to "tazweej" or "inkah" (marriage), as these terms are found in the Qur'an, and because marriage is close to acts of worship, the expressions for which are derived from the Divine Law.

Based on this, the guardian's statement "I have given" does not contract the marriage, even if it is accompanied by the husband's acceptance, for a contract is the joining of offer and acceptance. What transpired was merely a mutual agreement or an engagement (khitbah), and engagement is not a binding contract; either party may annul it. This woman is not your wife and does not need a divorce to separate from her; annulment suffices. After the annulment, it is permissible for others to propose to her.