I'm concerned as to what is commonly accepted of each main character; I wish to mainly focus on The Hero of Kvatch. You are able to do all of the Guild Quests and DLC's in one playthrough; but my biggest issue is solely caused by The Knights of the Nine DLC. How can one be The Grey Fox, The Listener, Sheorgorath and The Divine Crusader at the same time? Is the MC considered all at once?

History doesn't say that the same person did all those things. They all happened, but it isn't known who did them. It's more obscure again for the faction storylines in Morrowind because the player has contradictory choices. The Thieves Guild there appeared to be destroyed, but it might have just been driven deeper underground. Did the Nerevarine help the Fighters Guild destroy the Thieves Guild? Did he defend the Thieves Guild? Did he have anything to do with it at all? As of Oblivion, there are no definite answers to those questions available.

Because it's a video game.

What is commonly accepted is up to you, because it's your character in your game. The choices you make in-game are not relevant to canon.

Bethesda focused on giving the player content to play with, not if it made sense that they could all happen to one person in the history books of TES.

If you don't like how your character can be the Grey Fox and Sheogorath at the same time, you can do those quests on separate characters.
Maybe I'm missing your point, but TES games are about freedom of choices in a sandbox world, not a history lesson or biography on one person.

So as far as lore is concerned the PC is an independent variable? I was mostly asking to scope the grandeur of The Hero of Kvach.