Is reciting Al-Fatihah the correct and guaranteed method for engagement, or is it a mistaken step?

You have done well in striving for righteousness in your religion, but you have erred by confessing your love to your cousin, who is a non-mahram to you. What is obligatory is repentance and not returning to such an act. Marriage should be initiated promptly, and studying should not be an impediment.

If you are unable to bear the expenses of marriage, do not propose or contract the marriage if the period will be long, as this may lead to problems that could result in estrangement and mutual hatred.

If you are insistent on contracting or proposing now, ensure both parties agree. If the disagreement persists, prioritize obedience to your father, for honoring parents is among the obligations.