Old dng specification used 2 color matrices for conversion. However, all adobe profiles in last years are up to dng 1.3, where color conversion is performed using two forward matrices, while two color matrices are used for WB. So there are 4 matrices in total in dng profiles. So it's not the same workflow as in dcraw which is using these matrices a bit incorrectly (whitebalancing is performed differently). However, ACR will work up to old dng specification and use only color matrices if there are no forward matrices in profile or in dng. I studied it in detail, since I needed that to make my dng profile generator program that is still unmatched by adobe, although lately they came quite close with "v3 profiles", as I documented on ACR forum several months ago.
I suppose all chdk dngs have baseline exposure tag = 0.5, while this value is generally different for each camera, hence the exposure difference between cr2 and chdk dng. You can check the value of this tag in a dng converted from cr2, using exiftool utility. With the same utility you can also change it, so results will be the same.
dngs made from crw have no WB info, since dng4ps2 doesn't know how to extract this info from jpeg, because it is in manufacturer info tag, and it's position depends on the camera model. A while ago I made an utility to copy this value from jpg into dng for my compacts. Without that, WB set to "as shot" is the same as WB Auto in ACR
You can use lens profiles with every kind of raw/dng files in ACR, just you have to select it manually - if you have it for your lens. But lens profiles provided by adobe so far seem to ... well ... need some refinement ...