Non-compliance with the development plan by the neighbor

Then I would criticize him for his terrace as well..... He just built it there afterwards.... I am 100% sure that nothing is approved there at all. You usually don’t need approval for terraces here.

Everything a bit mixed up,...

Which state building code, i.e., which federal state?
What does the development plan say about it?

Is it legally even considered an ancillary structure, or at least a subordinate ancillary structure like a terrace roof?
(A spatial-functional use is likely always given; if necessary, only something about the floor area ratio might be objected to if it is exceeded afterward, but there may be political loopholes here, i.e., whether the ground is sealed at all by the covering. If it is a nature reserve.)

Is a neighborhood law affected at all?

The same applies to the fence; what neighbors agree on among themselves does not have to have legal validity. What regulates this period within 1 year after completion?

If you are planning a garden house, I know quite exactly where it would stand. You can implement that quickly if necessary.

The federal state is Lower Saxony.

The development plan states:

On the non-buildable areas along the water body, ancillary structures according to §14 of the Land Use Ordinance are not permitted.
I have already inquired out of interest and can say that a terrace counts as an ancillary structure according to §14.

In the Lower Saxony Neighbor Law, it states that there is an obligation to fence the right property.

What does that mean? "I would know pretty exactly where that would be stated"

That means the common border is the body of water?

The northern boundary of the properties runs along the water or shore.

The shared boundary is from our side the western one.
So all properties are in a row, and behind us is the body of water.

I hope I have written this understandably.