I transferred internationally through DME a couple of times last week (out and back) on S7 tickets. There is very little integration between S7 and the BA flights it uses from London, which have S7 codeshare numbers but have to be managed (seat choice and check-in) through BA.com with the separate BA PNR. You can check in and select a seat on the S7 website using their PNR but they do not issue a BP. BA at T5 were able to check my luggage through to my final destination (OSS - Osh, Kyrgyzstan) but could not produce the boarding pass for the second flight on S7 (Globus) metal.
It was very straightforward obtaining this at DME - follow the yellow 'Transfer/Transit' signs up the escalator, parallel to those heading for immigration, but at the top of the escalator there is a clearly marked S7 Transfer desk where you obtain the onward boarding pass (they will need to see your checked luggage receipt). This takes them some time but there are seats nearby and they will call you when they are ready. They will also issue an invitation to the S7 International Business Lounge if entitled, though this is not strictly necessary and I didn't need on on the return journey, just showing my card.
Once in possession of the BP they direct you through a small 'Nothing to Declare' door to the left of the (unused) passport booths where there is a desultory security check and a thorough look at your passport (UV, magnifying glass, the lot). Once past this you emerge into the airside international Departures area - turn left for the lounges. You cannot buy duty-free goods to take to Osh as apparently they have no suitable customs facilities there.
It was a similar experience on the return (and comparatively relaxing after the horrors of leaving Osh, though there was no problem checking my bag all the way through to LHR) except that printing the BP for the BA flight was a real challenge and they issued a temporary hand-written BP. The real thing was eventually delivered to me as promised at the gate several hours later.
There was never any hint that a Russian visa, either entry of transit, was required,