I don't think the issue of SVO or DME is so important as their stupid routing via DXB. When (if) they decide to offer nonstop from pakistan and they offer decent frequency (atleast 3x weekly) then they can think of moving to DME.
The reason this route is via DXB is because there is not much O&D demand between Pakistan and Russia. However, from what I have heard, load factors on DXB-SVO sector are well above 90%, so apparently they are getting a lot of 5th freedom traffic.
Have they refurbished it? When I was there in the mid-90's it resembled a scene from an old James Bond movie. Both SVO and DME were pretty decripid.
Yes, it was privatized and purchased by the East Line Group. They have completely renovated it and a number of foreign carriers, including BA, LX, EK, QR are now using it. It is now probably the best run airport in the former USSR and is the best run aiport in Russia.