We can get it checked. Could you share more details? Is it happening with a specific Ai file or all of them? Ensure that the Ai document is in RGB mode.
According to your AI screenshot, layer 9("Kalendar") in the AE comp should be layer 21. You must have deleted a bunch of layers. The other layer names don't match up either.
Select the Kalendar layer in Illustrator and look for the center of the graphic. If it is not in the center of the artwork in the layer, then you have some funky stuff going on in that layer.
Did you import as a composition retaining layer size?
I think cleaning up the Illustrator file so it only has the layers you want to use and ensuring there are not some weird clipping masks or groups in the layers will solve your problem.
In Illustrator your art is black and you don't have a background in your AE comp. Show the Transparency grid (the little checkerboard icon below the Comp panel) to see if your art shows up. If this is the case you just need to add a BG layer in AE.
Unless you explicitly created a white BG in Illustrator, that's just there for easier visibility and isn't a real background.
I don't think it has anything to do with the bg. Even if I turn transparency on, the layer simply doesn't include the art. You can see that, bc the AE layer shows the anchor point in the lower left corner. That usually only happens when the layer is empty. But the AI file includes the art. It works with older AI-files. In those, AE shows all art in the seperate layers. Any other suggestions?