I'll answer the question about rendering to specific slices of your texture array. Yes, that is how you would do it. You just need to set up a depth stencil view to each slice you want to render to, then set that to the output merger (OMSetRenderTargets) for writing out your shadow maps. After you're done with all of them (and have unbound them) set the entire thing with one shader resource view that can access the entire array.
At first thank you for your answers. Lets split it into two different problems:
I think the problem with the Tiled approach would be that I also have a Projection Texture AND Shadowmap. Finally I'm not sure about the maximum Texture Array size. Next question would be, is it possible to render the shadowmap directly into the array on a specific slice or to I have to copy the single shadowmaps into the array?
As I mentioned before, the current approach to render the projection (by drawing a frustum mesh) isn't really an optimal solution, because it waste a lot of GPU power. Please have a look on the attached Images. The first one shows a current approach and the second would be perfect, but I don't know how.
I also thought about an another approach for texture projection, please let me know what you think:
In a computeshader just use the shadowmap to reconstruct a worldPos, Project it back to Screenspace to figure out GBuffer coords and finally do the shading. But I think the problem here will be the undersamping/interpolation, because of fixed size of the shadowmap.