So what happens if I just go to the Aldmeri Dominion and I just kill everyone there? What exactly what happen? I'm just curious and want to know. I know there's probably going to be a large bounty on my head and I'm sided with the Empire. Sorry if it sounds like a noob question.
You can't go to the Aldmeri Dominion as it is not included in the game world.
I assume you mean the Thalmor Embassy. That destination is part of the main quest, and without console commands on a PC or other glitchy ways of getting in, much of it will be unreachable unless you are doing that part of the MQ that includes it and which gives you full access. If you do get to the otherwise inaccessible areas prior to entering them for the MQ, it's likely that you will end up with a bugged out MQ.
You can approach the Embassy grounds and the lock on the front gate is, as far as I know, pickable at any time... but it's unlikely that the Thalmor you can get to just by entering the grounds will be hostile unless you attack them. I went there after finishing both the CW (for the Stormcloaks) and the main quest and they still weren't hostile on sight, I had to attack them to make anything happen. They are probably programmed as non-hostile because they have to be that way when you are sent there on the MQ. If you have to attack them without provocation, I assume you will get a bounty unless you kill all of them and thus remove any witnesses.
There is also a group of Thalmor holding Northwatch Keep, farther to the west along the north coast in the same hold. You can pick up a side quest that will send you there and they will be hostile and you can wipe them out with impunity if you like.