The answer to all three of your sub-questions is "No."
The actual picture data from what the sensor has captured in a raw file is not affected by the in-camera processing settings. The preview JPEG file embedded in the raw image file is affected by those settings since the camera uses them to generate the preview JPEG.
When you view an image in Darktable using lighttable mode, you are viewing the JPEG preview, not a rendering of the actual raw picture data. When you go into darkroom mode then you are viewing a conversion of the raw data. This conversion is created by the program that probably doesn't even attempt to read the information from the raw file that includes what the in-camera setting were at the time. Even if it could read them, it wouldn't be able to do much with them. Unless a third party raw convertor, such as Darktable, has access to the exact algorithms used by the camera manufacturer then any rendering they do is basically a reverse-engineered educated guess. Most manufacturers make their demosaicing algorithms proprietary and either do not share them at all, or only share them with major players on the image processing software landscape such as Adobe (LR/PS/CS) and DxO Optics. And all Adobe products, to the best of my knowledge, ignore any information in a raw file that has to do with the in-camera settings. This information is, in fact, stripped away when a raw file such as a .cr2 from a Canon camera or an .nef from a Nikon camera is converted to Adobe's .dng format.