1.) Verkündigung - none of these really fits: Siehe Wörterbuch: Verkündigung
What is meant is quite synonymous to Greek "kerygma", cf. http://www.afn.org/~afn52344/kerygma.html
Therefore, my first choice would be "preaching", maybe "sermon" (but only in this case!)
"annunciation" seems completely wrong here; the term refers to announcing something to an individual or maybe a group of people.
2.) Stein geworden: set in stone, carved in stone, (maybe) become stone, petrified - all of these sound much more immovable and fixed than the German suggests.
So in combination it might be something like
- kerygma carved in stone
- preaching stonework
- stone(s) proclaiming the good news
- a sandstone sermon
The basic idea is one you would probably find in any work on church architecture dealing with the Gothic era that the Stehphansdom belongs to. Maybe there's an established English term, though none I would know of.