It is to their advantage after they get his data to (1) keep the US from finding out what they got from him, and (2) keeping him from giving that data to others.

Once Russia has what they need from him, they probably don't care what happens to him. Ship him back to the US, probably--that way they can try to patch things up diplomatically, and I imagine they have whatever they could squeeze out of him, intelligence-wise.

If we assume "etting Snowden fall into the clutches of Russian intelligence may be a far better deterrent to future leakers than a 'clean' prosecution and imprisonment here in the US", then surely if the Russians are capable of thinking long-term then treating Snowden nicely is in their best interest (why would they want to play into discouraging future American leaks?).

Depends on their belief in how my they've learned from him that we haven't independently figured out, normally you don't do that to make the counterintelligence game harder, e.g. does the US know all the methods he used to get his data? Plus if they want any future "defectors", as we called them in the bad old days, to come to them they've got to appear to treat him well.

Ship him back? He knows a lot about secure IT systems in the USA. If they are smart, they will keep him around to advise their own signals intelligence / hacker people on how to penetrate US systems. Maybe feed him some propaganda, help to push him a bit further over the edge (this is a guy who was at one time a big believer in the NSA, after all).

Why would they ship him back? That would be just a weakness. They can afford to keep him.

On the other hand, why wouldn't they hang onto him for a month or so, see if they can't extract information from him (not even talking about torture, there are much better ways of getting information from people), then ship him back to the USA or send him on his way someplace else. Long-term, he's served his purpose, no reason to spend a lot of money on him, especially if they want to smooth things over with the USA. And that's basically exactly what they're doing now: saying he can stick around until someone else claims him. Whether that's the USA convincing Russia to hand him over or some nation offering him asylum, Russia probably doesn't really care.

The Chinese didn't take his data.

How do you know? How, for that matter, does he? Given that China operates its own great firewall and that Chinese companies make a lot of network engineering products, I would not consider it a secure environment for digital information that I was anxious to keep secret.

I don't know of course, but that should be the default assumption. Parent stated it as fact without basis. It's unlikely that China can break encryption that the NSA has approved suitable for Top Secret data. If they can do that, they already have all of this information.

They could have made multiple stealthy visits and installed keyloggers, but that's also unlikely to work with him.

Put simply, if you work for both the CIA and the NSA in foreign countries as a technical employee, you know how to not get keylogged.