Clip Space in OpenGL and DirectX 12

I am implementing a custom mathematics library to create model, view and projection matrices in OpenGL and DirectX. I am doing this, to improve my understanding in the mathematics behind 3D applications.

At first I took a look at right-handed and left-handed coordinate systems. I realized, that if I create my view matrix as well as my projection matrix with the same handedness, the scene renders correctly no matter if I use OpenGL or DirectX (except inverted translation/rotation/etc.). This is a bit confusing because every article I read pointed out, that OpenGL uses a right-handed and DirectX a left-handed coordinate system. Is my assumption right, that the coordinate system completely depends on the handedness of the view and projection matrices?

When I took a look at clip spaces, things became more difficult to understand. The articles stated, that the clip volume on the X and Y axis ranges from -1.0 to 1.0 in both APIs. On the Z axis OpenGL clips from -1.0 to 1.0 and DirectX clips from 0.0 to 1.0. However, in OpenGL the scene renders correctly no matter if I use a projection matrix for clipping between -1.0 and 1.0 or 0.0 and 1.0. In DirectX only the projection matrix for clipping between 0.0 and 1.0 works. If I use the other one, nothing is rendered. So my question to this topic is: Can the clipping volume be changed on the Z axis or are those fixed implementations. If they are fixed, then why can I use both types of clipping volumes in OpenGL and only a single one in DirectX?

However, in OpenGL the scene renders correctly no matter if I use a projection matrix for clipping between -1.0 and 1.0 or 0.0 and 1.0. In DirectX only the projection matrix for clipping between 0.0 and 1.0 works

OpenGL renders because [0.0, 1.0] falls within the range [-1.0, 1.0], but DirectX does not because [-1.0, 1.0] can fall outside of [0.0, 1.0]. If you invert the depth of your test scene, you'll likely be able to see stuff in DirectX using the wrong projection matrix.

Can the clipping volume be changed on the Z axis or are those fixed implementations. If they are fixed, then why can I use both types of clipping volumes in OpenGL and only a single one in DirectX?

No, you can't change that behavior as it's part of the spec. The point of all the transformations you do as part of the rendering pipeline is to get your scene into clipping space. That means, for example, mapping your scene's depth from [-9999, 9999] down to [-1.0, 1.0] for OpenGL, or [0.0, 1.0] for DirectX

Is my assumption right, that the coordinate system completely depends on the handedness of the view and projection matrices?

Not sure what you're asking here. You already observed that a scene in OpenGL looks inverted in DirectX if you don't account for the difference in handedness. The view and projection matrix that your application uses doesn't change the behavior of the OpenGL and DirectX implementations.