[Jan-Poo]

They watched the human history of EP3 until the year of 3.598 AD, when a meteor destroyed earth. Then EP4 starts

Spoiler for up to ep4 translated:

Yes that's what i think. Everytime a an episode ends a new kakera materializes based on the outcome of that episode. A Kakera materializes in both space and time, and therefore the future until the end of the universe (for that kakera) is already set. I think something like this:


Original Kakera------------------ Loop |----------------------------------------- <- Kakera after ep1
-----------------------------|--------|----------------------------------------- <- kakera after ep2
--------------------------------------|----------------------------------------- <- kakera after ep3
--------------------------------------|----------------------------------------- <- kakera after ep4

However only those who can look in the future can know the future of a certain kakera, like Bernkastel, for example. At the time a new Kakera is formed, Bern can automatically see the whole thing. So she took her new chess piece from the newly formed kakera from ep3, and she took her at the time that piece became a "witch".

As for why Mammon remembers the "future" i still stick with the idea that its' Gretel's perspective that is influencing the stake.