Let's say the group is on a 20 days journey. How do you play it out? Like "5 days has passed and you're now setting a camp at night. / Roll Fatigue Test/" Telling them how many days passed and some overall stuff between fatigue tests? Or do you have some other ideas for it?

I have them roll, then depending on the result of the rolls collectively we describe that leg of the journey. If everyone passed with no issues we describe the agreeable weather and/or terrain and how their traits and preparation paid off. If they all roll terrible and gain fatigue, maybe they got lost. Often Players will pick on their on character and state that they packed too much or were over confident.

As the Lore Master I see my roll as the final voice on what happened, pulling the ideas together or maybe weeding some out, offering suggestions etc. It's not MY game or the Players game so we try to build it collectively.

If someone rolls an Eye I determine (in advance or on the fly) what that roll represents and then the appropriate tests are made and the narration continues. Occasionally this will be dealing with a specific event, like crossing a swollen river, unexpected chasm or attack by wargs or goblins.

Admittedly with new players, players from more traditional games like D&D or quieter players this can take a little coaxing. In those cases I try to script a few ideas into my notes when I prepare. I find that 50% of the players in my group really grab onto the creative moments and run with it. Sometimes I will prompt the other players for input. I try not to dwell on it too long if they aren't interested or run with it if they are in the mood for that type of play.

When we are done playing we always try to have a 30 minute chat about what worked and what didn't so I can get feedback for next time.

Some nights this works great and others it falls a bit flat. Really depends on the mood.