Would a girl accept marrying her paternal cousin, despite the abuse she and her parents have suffered from some relatives, their attempts to tarnish her image in front of the suitor, and her fear that these abuses will continue after marriage?

If your paternal cousin is a righteous young man who is diligent in his prayers and has good character, then seek guidance from Allah (istikharah) and accept his proposal. This is based on the Prophet, peace and blessings be upon him, who said: "If someone whose religion and character you approve of comes to you, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption." You must ensure his uprightness and his commitment to prayer. If that is the case, then he should not be rejected due to your family's greed or their dislike for you. Hold fast to Allah and rely on Him. There is no harm in some of your family members discussing with him to confirm his conviction to complete the marriage and his disregard for slanders. And supplicate frequently.