After I just gave a warning about being respectful, this was a really poor choice of wording.
Yes to all of them. What I want to know is how different are they from FATE?
Do players still take turns at being the allmighty?
Yeah, I'm a big fan of FATE. And, I find your "take turns being the almighty" is so inaccurate a conception that there's not much that can be done before that's dealt with.
In FATE games, the players have
a little more control than in many traditional games. They never get to "be the almighty".
How is actually sharing responsibility so much better than having one person to coordinate everything?
Oh, that's easy - Each of us, as a player or GM, has a personal style and habits. We don't tend to step far outside our habits. That places a limit on the creativity that will be seen in the game. Opening up a little responsibility to others allows their creativity to also play a part, and with a little practice, that means the game becomes overall more rich and creative.
How do you avoid the "I Win!" button, because other posters with much more experience, and much recent experience have seen it too. And not just one/once.
Not having read their detailed accounts in detail, I cannot be sure. Even if I had read them, I could not be sure - if they were a player, they probably don't know in full detail what was happening behind the screen.
We can say that, just like any other game, you need to build a bit of system mastery to run Fate well. And, just like a GM for D&D can build a softball encounter, or flub on a mechanic, a GM in Fate can do the same, and forget the mechanics that are at their disposal to adjust or recover when they see it happening.
One of the mods from some years back, username of "Rel", and I attend a house-con most years, in which folks are usually not running D&D. They are running games most folks haven't played before. You sit down for four hours, with a ruleset you don't know, haven't reviewed, and is explained to you in 10 minutes or less. That's not a lot of setup. So, Rel took to adding to his introductions a quick statement of "How to find the fun in this game."
Here's a hint for Fate - "achieve tactical domination" is not the way to find the fun in Fate. The game is a little less about the destination, and more about the journey.