Is it permissible to love a Christian with the intention of inviting him and guiding him to Islam, while abhorring his religion? And is praying for his guidance considered a sufficient means of communication in this case?

Loving a disbeliever for a worldly matter does not contradict the doctrine of Al-Wala' wal-Bara' (loyalty and disavowal). However, an emotional relationship with a non-Muslim is forbidden due to the concern that it may lead to an appreciation of their religion. The desire for their guidance is a good thing, and supplicating for them is permissible. As for inviting them to Islam, it is preferable that this be done by a man knowledgeable in Islamic law, to avert the temptation of a private meeting between a woman and an unrelated man.