Yes - you get DX mode NEF's just fine. Toggling the DX crop mode on or off has no affect at all on the file storage options you have selected on a D800. And no, while obviously there are many other reasons you might want to hang on to your D7000, if getting NEF's with a DX lens is the only reason you would keep it, then all of your needs are better met with the D800.
Now aren't you glad you got one??? I sure am happy I did! You are going to love it.
NEF file size reduces with format selected. ie. FX > 5:4 > 1.2X > DX
My view is if I have the glass I will use it. I use my DX 10-24 lens in FX mode. From 24-18 it uses the whole frame, bonus. From 17-10 the vignette gets progressively worse. Cropping in PP I always end up with the same or bigger image than DX mode would take.
In DX mode the viewfinder crop lines act like the guide lines on range-finder cameras. You can see what is just outside your frame.
Disclaimer: No centre IQ was harmed in this story. And a 16-35mm VR lens is on my wish list. Now to sell all my DX gear.
"We don’t see things as they are, we see things as we are" - Anaïs Nin