Different saturation between the development modul and fullscreen preview in Lightroom CC

This difference has not much to do with the color space used in Develop. What you are seeing is a difference in scaling algorithm used to display in the Develop module and in the preview. This will only show up in highly detailed images with strong color. The fall color in the tree to the right is a prime example of this. It is something to be careful with and is caused by the inherently lower resolution of your display than the actual image and the Develop module in order to stay fast using a subsampled version of your raw file so that it doesn't have to render the full resolution and then downscale every time. When going to full scale, it uses a higher resolution version of the raw to scale and you will get more blurring of the color. This is more like the actual export will look. This issue also crops up in night photos of the milky way and other highly detailed (or noisy) types of images.

Yes, this is true and there are no settings to 'fix' this. If your monitor can be set to AdobeRGB, then what you could try is setting the monitor to that and then select AdobeRGB as monitor profile (or create a new monitor profile). That means your develop preview will be 'translated' and shown in AdobeRGB on your monitor by the color management system, so it should display the same as the library preview, which is already AdobeRGB.