Dismantle basement window and seal it with concrete

Yes, just regular mortar. You push it in there with a pointing trowel. If it is a bit drier, you can compact it better.

What about [Quellmörtel]? Wouldn't that be better?

Source mortar does not "swell" in that sense. It is just particularly dimensionally stable and not necessary for your purpose. If you are going to do masonry anyway, just fill the last gap as well. There is really no need to make rocket science out of it. If it absolutely has to swell, you can also use construction foam.

Would you also take Kalk sandstone or rather another building material or stone?

Yes. Do it the way Karsten described in #7, that fits.

If I could now still find the strange holders described and give the stones support in the recess