So, I did kill Alduin now, after that I did help Ulfric win the war. Ulfric did talk about some moot, to make him high king, and some war comming up with the Tamriel.
I did start the Dark Brotherhood questline for now. But what do I do after that? Will there eventually be a moot, making Ulfric to High King, and a war with the Tamriel? Or is that just said to be held in some later version of Skyrim comming up?

There is no continuiation of the civil war or main quest right now. Maybe there will be in DLC, maybe there won't. I don't think we will see anything like this.
What to do now? Play the other guilds that interest you. Or set your own goals (learn every shout, get every daedric atrifact, become Thane of all cities...)

Ok. =) Thanks for the quick answer.

Just explore. Visit random towns and talk to random people. Way more to do that just the quest lines you've done. Way more places to discover and loot to be found. Just play.....

Save twice, use one save to Kill everyone in every town, and take over Skyrim yourself, the other can be your continuation when DLC is released