Is it preferable to slaughter the 'aqiqah for a male newborn on the day of 'Arafah – with the ability to offer the 'udhiyah if the 'aqiqah is canceled – or to cancel the 'aqiqah and offer the sacrifice for Eid? And what is the ruling if the matter pertains to a vow instead of the 'aqiqah?

If the choice is between sacrificing a sheep as an Eid sacrifice (udhiyah) or an aqiqah (for a newborn), then it is better to make it an Eid sacrifice. If the choice is between sacrificing it for a vow (nadhr) or as an Eid sacrifice, then sacrificing it for the vow is better, because it is an obligation, especially if the sheep was specifically designated for the vow, or if one does not own any other sheep and the time for fulfilling the vow is pressing.