Hello Minusch83,
Your construction project does not pose any technical difficulties, lowering the extension, the roof terrace, all no problem - for construction professionals; but I always find it difficult when tips for carrying out construction projects are expected from laypeople in a forum.
Example: "Earthworks" sounds quite simple, but there are different types of soil: sand, loess-containing, rocky, mixtures that allow water transport, those where water does not drain... all of this influences construction costs through the storage of excavated earth, the design of the excavation pit, the sealing of earth-contacting walls, earth pressure, and the associated construction of the walls, etc.
For the building permit/approval, it is best to inquire at your municipal administration. Everything else should be requested from a local architect; he does not have to supervise the entire construction project.