Is the marriage valid if a man marries a Filipino woman after her father agreed to make him his agent in marrying her to himself, and with the presence of two witnesses to the marriage?

If the woman's guardian agrees to her marriage and appoints you as his agent, the agency is valid and does not require witnesses. Your direct performance of the marriage contract is valid, in the presence of two witnesses, by your handling of both sides of the contract.

However, if the guardian's consent is not obtained, the marriage is invalid according to the majority of scholars, but valid according to Abu Hanifa and can be upheld judicially.

If the woman is a non-Muslim, for her marriage to be valid, she must be from the People of the Book (Jewish or Christian) and chaste.