Is it permissible for a young Muslim man to marry a Filipino Christian girl whom he loves and promised to marry, and whom he taught some matters of Islam, and she is convinced of Islam and wishes to convert to Islam after marriage so that it would be a proof before her family, knowing that his family rejects his marriage to her?

Marrying a chaste woman from the People of the Book is permissible, and it is even desirable if there is hope of her embracing Islam. If your father refuses your marriage to her, then leave her, unless her absence would cause you harm. It is obligatory to cut off your relationship with her if she is a foreign woman [unrelated by marriage or mahram (definition)], and inviting her to Islam should be done through righteous women or legitimate means that do not involve temptation.