Is marriage to a Jewish woman in occupied Palestine, in the manner mentioned (offer and acceptance without official documentation, and without her converting to Islam), permissible? And is it originally permissible to marry her if you both agree to raise the children in the Islamic faith?

Marriage to a chaste Jewish woman is permissible, but it is preferable to marry a woman of faith and good character. What occurred is not considered a valid Islamic marriage (nikah shar'i) due to the absence of its essential pillars (the guardian and witnesses). Therefore, the relationship with her must be severed until a valid Islamic marriage contract is performed, fulfilling all its pillars and conditions, including the guardian's permission and presence or the appointment of a representative, and the presence of witnesses to the contract. It is not a condition for it to take place in court, but it should be documented there to safeguard rights.