Terrace planning for a corner terraced house with a large garden - What to consider?

I actually called and wanted to clarify it in advance, but the office does not work properly, gives no information,... everything has to be done in writing.

THIS is proper work, to do it only in writing. That is then binding and verifiable. The next step in the objection procedure would be the lawsuit. How do you want to base it on an oral statement?

Your building authority is not special; it adheres to existing laws. And those are non-negotiable. You are not at a bazaar there. Of course, you can ask something beforehand, but it would be of no use to you because it is never binding. If there is a 3 m limit, you cannot negotiate to 3.5 m. Limits have a purpose. If they approve 3.50 m for you, then the next person will want 3.60 m. And so on. I doubt whether you would really be allowed to plant cypresses 3 m high at the boundary; usually, the limit is 2 m in height.

They allow me to build the terrace roof to a depth of 3m, but not 4m.

There is absolutely nothing against it

Yes, the law.

and usually you get a special permit for a construction project like mine, too,

Usually, one adheres to regulations. What you are getting is a big concession.

I have the house positioned so that when I go onto the terrace, I have the building boundary at 150 cm. They allow me to build the terrace roof to a depth of 3 m, but not 4 m.

So they are already permitting you to exceed the building boundary by 150 cm ... and now you want 100 cm more.

Get advice first, so they don't revoke your current exceedance. More sealed surface area means less space for rainwater infiltration.

Is the roofing allowed to be on the neighbor's boundary?