Is a penthouse allowed if the development plan requires a flat roof?

If the development plan says "II FD"

If the Roman numeral two is circled, this is a mandatory requirement according to the planning symbol ordinance, i.e. it must be built with two floors. A recessed floor would then only be possible under the conditions mentioned by Yvonne in #7. Otherwise, it is a maximum limit, meaning one can also build with one floor or with any size of recessed floor.

Up to what slope is a roof actually considered a flat roof?

I am not aware of any legal regulation, neither at the federal nor at the state level. The legislator probably wants to give the approval authorities some discretion. Like , I would see the limit at 10°, but in case of disagreement with the building authority, a court would ultimately have to decide in the individual case.

The legislator apparently wants to grant the approval authorities some discretion. Like , I would consider the limit to be 10°, but in case of disagreement with the building authority, ultimately a court would have to decide on a case-by-case basis.

I hope that the municipality clarifies in the textual provisions how it interprets the term.

If the Roman two is circled, according to the plan sign regulations it is a mandatory provision, i.e. it must be built with two storeys.

I believe the OP is asking whether "two full storeys" – regardless of the "measuring stick" for the respective state building code's full storey definition – usually means that a third storey is indeed permitted, only just "smaller," and in connection with a flat roof according to the development plan, therefore also allows a "third" storey with a horizontally limited upper boundary. In other words: whether an equivalence of a flat-roofed recessed storey with a pitched-roof attic storey can be assumed.

And to that I said - first: basically "yes," with the note that due to the flat roof characteristic "eaves height almost equals ridge height," the eaves height limitation is the critical point; - and second: that in relation to the floor area ratio / floor space ratio, the answer can sometimes already be read. For example, 0.2 versus 0.5 suggests that one can use the "remainder" of 0.1 for a half-sized attic storey; whereas with 0.2 versus 0.4, a remainder for more than a second storey only arises if the floor area ratio is not fully utilized.

I hope that the municipality explains in the textual regulations how they interpret the term.

That would be desirable, but I have never read that.

0.2 compared to 0.5 suggests that the "rest" of 0.1 can be used for a half-sized attic

That presupposes that the development plan explicitly requires the calculation of non-full floors or that the development plan is older than 27 years. Otherwise, the floor area ratio is only calculated in all full floors. As so often, an excerpt from the development plan and the textual regulations would be very helpful.

That would be desirable, but I have never read it.

I can't say exactly where. But to my recollection, it was a development plan I looked at within the last two months because of a local thread. It mentioned something about pitched roofs up to 10° pitch being considered flat roofs. I believe even without the addition that they would have to appear completely horizontal with a parapet. But yes, unfortunately you don't often read that. More recently, however, one increasingly often finds that the desired types of front garden bushes are listed in painstaking detail. It seems to me that some municipal administrations have special breakfast directors for that.