Is it permissible to marry a Christian girl who has declared her conversion to Islam and whose Islam is good, but whose family refuses the marriage because she was Christian, knowing that the girl is exposed to harm and torture from her family if she does not marry?

You should persuade your parents to agree to your marriage to the girl with wisdom and gentleness, and seek help from someone who has the ability to persuade them, and clarify the girl's adherence to Islam. Your parents' objection is not legally permissible, and Islam overrides what came before it. If the parents do not agree, then, in principle, their obedience is obligatory. However, if not marrying the girl would lead to a significant harm, such as her being tempted away from her religion or being subjected to torment, then there is no harm in marrying her, in accordance with the principle "warding off harms takes precedence over achieving benefits," while still trying to appease the parents.