Is it permissible to marry an American Christian woman sacramentally (on paper only) in order to obtain a green card, without intending to consummate the marriage, with the aim of facilitating visits to her country and helping parents in the home country and working with one's degree?

This is not the purpose of marriage in Islamic Sharia—to marry for the purpose of obtaining residency rights and then divorce. What is apparent is that it is impermissible. Furthermore, merely contracting marriage on paper with a Christian woman is a deception against disbelievers, and this is not permissible, as Allah عز وجل does not approve of injustice.