I can add a bit about the oranges if Pugi doesn't mind. I couldn't tell you what is authentic to a specific region like Pugi can. My grandfather was from Delicias, MX. All of the stuff we do and the wqay we do it, we learned from him. One idea behind adding the juice from fresh oranges is to do so at the very end of the cook. The idea is to get the sugars in the orange to "carmelize" and add some color. The bad part is that if you add too much or add it at the wrong time, the sugars burn and you get that burned taste on the meat. Around here, the mom and pop shops sell their version of carnitas which are 3-4 square chunks of pork that are deep fried. The outside is crispy and basically you tear off/shred em and go from there. Pugi is right, every region adds their own touch to it.
Here's how we like to do it: