I'm overloading both of my braincells trying to figure out what I'm even looking at

It's a common or garden variety windowsill, related to many different types of windowsills you might see around your neighborhood most times of the year.

No idea what specie has taught you to photo, but I don't have the slightest idea what I am looking at.

My dibs would be on MTB (birota montium) on the left and its road sibling (birota viae) on the right :)

Probably something like these

Probably some sort of Orthoceras. https://en.wikipedia.org/wiki/Orthoceras

The grey/green stone on the top of your picture looks like marble. Marble is a metamorphic limestone, which means that recrystallization occurred, which means that you should not have fossils in it as much as in sedimentary limestones.

So maybe it's not a fossil but a trace of the excavation process? Is the stone as smooth as elsewhere in this area?

That being said, some very old limestone can be denser than marble without being recrystallized. I just don't know of any that aren't grey or beige.