2 – Eating before going out to pray on Eid al-Fitr and after the prayer on Eid al-Adha:

Praise be to Allaah.  

Part of the etiquette is not to go out to pray on Eid al-Fitr until one has eaten some dates, because of the hadeeth narrated by al-Bukhaari from Anas ibn Maalik, who said that the Messenger of Allaah (peace and blessings of Allaah be upon him) used not to go out on the morning of Eid al-Fitr until he had eaten some dates… of which he would eat an odd number. Al-Bukhaari, 953. 

It is mustahabb to eat before going out to emphasize the fact that it is forbidden to fast on that day and to demonstrate that the fast has ended. 

Ibn Hajar (may Allaah have mercy on him) suggested that the reason for that was so as to ward off the possibility of adding to the fast, and to hasten to obey the command of Allaah. Al-Fath, 2/446 

Whoever does not have any dates may break his fast with anything that is permissible. 

But on Eid al-Adha it is mustahabb not to eat anything until one comes back from the prayer, so he should eat from the udhiyah if he has offered a sacrifice. If he is not going to offer a sacrifice there is nothing wrong with eating before the prayer.