Great, many thanks for the many answers. I will try to summarize again:
1) Topic weight: With a kit weighing about 500kg, you will see no problems on Styrodur and corresponding screed.
2) Topic air pressure monitor: To be clarified with the district chimney sweep; all elements that exchange air must be considered, such as the range hood, for example.
3) Topic expansion joint: Do not tile over this, but integrate it into the tile pattern and thus also depict the expansion joint in the tile design. If it is exactly this kit, the size of the screed recess suggested by the manufacturer should also be chosen. It is not yet clear to me why one should not take a buffer (of 10cm or 20cm), provided it is covered by visual components of the fireplace?
4) Topic power (7kw): The fireplace will be oversized for our house, so it will get very warm very quickly. Do not run the fireplace at 50%, but always fully to avoid shiny soot and tar deposits. It is feasible, just warm; here, possibly compensate by an open staircase and open first and second floors.
Is that correctly understood?
Best regards,
Sebastian