Is it permissible for a Buddhist girl to declare her Islam and utter the Two Testimonies of Faith before fully believing with her heart, and is it valid to marry her in this case?

A disbeliever does not enter Islam unless they believe in their heart and utter the two testimonies of faith (Shahadatain). Mere utterance without belief does not admit one into Islam. So, if a woman utters the two testimonies for the sake of marriage without belief, then her marriage is not permissible. However, if she utters them, and one does not know whether she is sincere or not, then the default is to believe her and apply the rulings of Islam to her, including marriage.