Is it permissible to marry a girl who believes in Allah, His books, His messengers, and Islam as a religion, but has not pronounced the Shahada due to her incomplete conviction in some principles of Islam, such as the punishment for theft or the prohibition of alcohol? And how can one ascertain her complete faith to raise children upon Islam?

It is not permissible to marry a non-Book (non-Abrahamic) disbelieving woman until she embraces Islam, based on the Almighty's saying: "And do not marry polytheistic women until they believe." Her Islam is not established until she pronounces the two testimonies of faith (Shahadatayn) with their conditions. Pronouncing the two testimonies of faith is of no benefit if she denies any of God's prescribed limits or any unanimously agreed-upon ruling, because Islam is only affirmed through submission and obedience to the texts of the two revelations (Quran and Sunnah (definition)). If she pronounces the two testimonies of faith with their conditions, practices the rituals of Islam, and her Islam is good, then she will be a righteous wife. However, if she persists in refusing to pronounce the two testimonies of faith, or pronounces them without conviction, or does not accept God's prescribed limits, she is still a disbeliever, and it is not permissible to marry her.