1. Whenever Nativity falls on a Sunday or on a Monday, the Royal Hours are done on the Friday before. Thus, the GOA parish is doing it incorrectly. The Liturgy on Saturday morning is that for the prefeast (paramon).
2. The vigil at your Antiochian church begins at midnight which is the prescribed time for the vigil and the Liturgy. Unlike the Western Rite, where there are Masses for Christmas Eve, Christmas Midnight, Christmas Morning and Christmas Day.
3. As far as fasting goes, there is no one strict rule, though a strict would be unwise since you would do so from Friday midnight through Sunday midnight. I would recommend a light meal after the Liturgy on Saturday morning and, according to your strength, fast until the Eucharist from the Liturgy for Nativity. Of course, all that should be cleared with your spiritual father.