Is it permissible to sit with and shake hands with a Christian woman for the purpose of convincing her to embrace Islam and marrying her? And is it permissible to be lenient with her in these matters to avert the harm of her disbelief, especially if she is very close to Islam and it is highly probable that she will convert?

It is forbidden for a Muslim to establish a relationship or friendship with a foreign woman, as it is a path to adultery and sin. Similarly, shaking her hand is forbidden by Shariah. It is not permissible to be lenient with Allah's commands to justify shaking her hand by convincing her to embrace Islam or by marrying her. The داعية (caller to Islam) must align his actions with his words. And whoever desires marriage should not base his relationship on sin. Therefore, one must stay away from this Christian woman and sever all ties with her. The داعية can seek assistance from his female Mahrams (unmarriageable kin) or through correspondence to invite her to Islam.