Does the obligation of Zakat al-Fitr become lifted from me if my father pays it in cash outside the country and from the beginning of Ramadan, given my ability to secure food for a day and a night, and knowing that I am Hanbali and my family is Hanafi, and I am unable to pay it myself in the form of food?

If you possess food in excess of your needs for the day and night of Eid, equivalent to one sa‘, then Zakat (definition) al-Fitr becomes obligatory upon you. You must give one sa‘ of wheat or dates to a poor person in your area. If your father pays it on your behalf in cash, there is no harm in adopting this opinion and following those who issue such a fatwa (definition).