Is it obligatory for me to fast as expiation for breaking an oath after I swore in a state of anger that a girl would not fail, and she did fail? And am I required to re-fast the full three days if I intended to fast them for expiation, and I fasted the first day, then I slept past the intention for fasting the second day?

If a person swears by one of Allah's names or attributes concerning a future matter, based on their belief in the truth of their expectation, and then what they swore about does not occur, the majority of scholars hold that expiation (kaffarah (definition)) is obligatory. This expiation consists of feeding ten poor persons, clothing them, or emancipating a slave. If one is unable to do so, then they must fast for three consecutive or non-consecutive days.

Some scholars are of the view that nothing is due from him, because he is merely expressing what is in his heart.

If anger does not alter the awareness of the person, then the oath is binding. However, if they are unaware of what they are saying, then nothing is binding upon them.

If you intended to fast for an expiation of breaking an oath and you fasted for one day, you must complete the remaining days and do not repeat the day you have already fasted.