I would like to complete every quest using the Dark Elf.

Good luck - Skyrim generates its own quests
I suppose it's possible to complete the non-repeating quests with one character, but I wouldn't recommend it. It's far more enjoyable to spread them out over a few characters - would one person really be an assassin, mage, scholar, thief, warrior and prophecized hero?

ya its pretty easy to do all the non repeating quests, and make a character balanced enough to do everything (although you won't be restricted by your skillset in a guild anyways) Only a few questlines lock eachother out that i'm aware of. You have to pick a side in the civil war, and you can't destroy the dark brotherhood if you join them

I have, there maybe a couple Radiant Quests, but those don't really count. The only quest I've ever missed out because I've never heard of it is "Rise in the East" in Windhelm.