It is necessary to "culotte" before the first use. You will find the look you are talking about by the patina. You don't wait for it to form but it is the result of a treatment of your stove.

Depending. I recommend the treatment according to Pfannenhelden.de: Bake six times rubbed with linseed oil. This gives a good base coat that strengthens with each use. Do not clean with soap or heavy scrubbing.

Before using the pan for the first time, it must be baked with él. Search engines and video portals have instructions on how to do this.
Or here directly from de Buyer --> https://www.debuyer-brandshop.com/de-Buyer-M...
It does not have to be the oil from de Buyer.
The patina will increase with each use.

Quite quickly, but the pan becomes more and more cultish with time, so more and more pleasant to use.
There are a few precautions to be taken though, follow the recommendations for the start and avoid acidic foods (e.g. tomatoes!) which remove the cullet very quickly.