It depends how you define everything... as in do you mean just the quests and places, then yes by
reloading your past save. But if you want 100% completion, including every single rare item then no. It's impossible. Your choice can affect the reward you get from a quest, and a lot of quests reward you with enchanted items. You cannot get keep every single enchanted item from a quest if there are multiple because your choice allows you one. Not to mention there's possibly 100 oblivion gates, of which only 50 will randomly spawn across the map per new game, and if you've closed more than 20 when you give Martin the Amulet, no more will open.
Some quests are also continuous with no ending (e.g. Grand Champion Arena fights, giving madness ore/amber material to the blacksmith for armors)
I can't even imagine how long it might take to solve this game multiple times, there are so many quests and areas...
Not even half as close to the time it'll take you to do everything on one character. I don't mean this rudely, but you clearly have no idea just how much is in this game if you think it's faster on one character than multiple.
- Some quests have multiple outcomes, and outcomes at several stages of the quest. I don't just mean the main quest line of Cyrodiil and Shivering Isles.
- Having to constantly save during these quests which can be long themselves will eventually become tedious, and if you forget you may end up redoing a hell of a lot more than just your choice. Considering the amount of quests, do you really want to do that?
- The choices you make during a quest can affect the dialog in the entire game. Another quest can also alter this dialog further (e.g. if you were lawful when you did KOTN quest line the dialog will change but gaining infamy points will change it further), If you want to hear all the dialog, then it'll be hell to finish on one character.
- There are a total of 60 oblivion gates to shut - 50 randomly generate, 9 standard ones, and one great gate.
- The guilds that can take ages to complete as they have their own outcomes too
- There is an extraordinary number of Ayleid Ruins, caves and forts on top of all this
- The Shivering Isles is only linked to Cyrodiil by a mysterious door. It is a whole new area with its own main quest line, forts/caves/ruins etc, artefact and rare items.
If you are really that concerned with a time efficient way to complete this game, then don't do it all on one character. You have no idea just how long it'll take you to do everything on one character. At least with multiple if you actually role play with this game you can do all the good stuff on one character, all the evil stuff on another (examples if you want simple rp) and you've technically done all, not to mention you can have a chance at getting each quest reward.
Having multiple classes means you can pick a race and class that gives you the ideal boosts and resistances to make your specific role play storyline go much smoothly than having one class do something it may not be ideal for.
P.s. if you want absolutely everything, get the 9 official plug-ins as well. 5 of these grant you new places which become safehouses once you complete the quest they each provide, KOTN is one of the expansion plug-ins, 1 adds brand new powerful spells to the game, 1 grants armor for your horse to aid it's survivability, and 1 puts in the largest dungeon in the game, with quests and it's own item.
As others have said, yes you can but I can not understand why anybody would want to, but maybe that's just me.
You aren't. LIke Glargg said there is no wrong way to play a game like this, but personally...I find it weird that someone would a role play game that gives you as much freedom for your character as this series and not role play with it.