Is it possible for you (even on a console) to change an NPC follower (or companion)'s outfit to anything you want? I've seen people with matching armor with a companion and stuff of this nature. Does anyone have the answer to my question? Step forward!

Talk to them and say "I need to trade equipment with you"

Companions will automatically equip the best armour available. For example, Lydia starts with steel armour. So at some point I got lots of dwarven metal ingots, and crafted 2 full suits of superior dwarven armour. Gave one set to lydia, who immediately equipped it. That's how you get matching armour.

So if I find a companion with a nice face (Lydia for example), I can give her like Forsworn tribal "armor" and she'll wear that? And would she keep it on or change automatically without me giving her anything else?

Well, it depends. If she gets a better armour rating (or at least it's flagged as better armour), then she'll put it on. I found that the change was instant, and she'd keep it on until you asked for your equipment back or until there would be better equipment. But she always has a minimum of steel armour.