DNG does in fact store WB settings. As it is a raw format, one can generate different images using other WB settings, but the original setting is in fact stored in the DNG. (Other RAW formats may very well not store the WB setting, i don't know)
However, there are other settings that the camera engine uses for the image generation that are not stored with the image. For example "colour saturation", i fiddled with this setting in Lightroom, and noticed that the a very low saturation generated a similar image to the camera's JPG.
Correct, there is a WB setting in DNG (and in other RAW formats like CR2). My understanding is that the initial WB setting in the DNG is set by the camera when it takes the photo. As I said before, in my experience, the WB on the JPG is the same as the WB on the DNG file when I load it with ACR.
As you said, not all settings are transferred to the DNG. As far as I know the sliders on the DX-1G for in-camera sharpening, saturation, and contrast are only applied to the JPG files, and not the DNG files. Once you make adjustments to the DNG in a program like ACR, it stores those development settings with the file (or in the case of CR2, a sidecar file).