Also, are there any clarifications what exactly are: Model-Space, View-Space, Camera-Space? Are they exactly as I told?
Model space or object space, is the space in which your mesh is defined. When you load your mesh, each vertex is in model/object space.
Eye,view or camera space , is the space around your camera, with the camera position (center of projection) being the center (0,0,0).
The common transformation is
objectspace ==model-transform==> wordspace ==view transform==> viewspace ==projection transform ==> screenspace
When using deferred rendering, the g-buffer is typically in view/camera space.
But how do I need to calculate Positions texture?
If you are in camera-space, you only need to save the depth, that is all. You dont need the position, because you can reconstruct the camera-space position from the screen-pixel position (aka fragment position) which is available in the fragment/pixel shader and the depth (there are different approaches to do it, best to use the search function/google for more detailed informations).