When did Russia start getting nervous about China so close to its borders?
Around the time that Mao had consolodated his power and was no content to continue as junior partner in a Soviet-led international Communist entente, from what I can tell.
Why do you suppose the US and Europe didn't do more to stop Mao from beating the other guy, sounds like Jeng Ki Shek?
Well, what more could they have done? Invaded? They supported the Nationalists to a similar extent as the Soviets supported the Communists - it was more a matter of the Communists having the advantage on the ground. The Nationalists had legitimacy and popularity issues to begin with, and are supposed to have taken much heavier losses than the Communists against Japan in WWII (although there is much revisionist history since then trumping up the Communist role in that conflict).
As for other related factors: not so much "communism" as such, but there is a geographical factor in the degree of centralization (both political and economic). This stems from how well suited the geography of a country is to defense and movement of goods. The USA is generally held to exhibit among the lowest pressures for centralization, because the country is secured by two huge oceans (so you don't need much standing army to defend yourself, on the day-to-day) and because a huge portion of productive lands are linked together (and to the sea) by navigable natural waterways (i.e., the Mississippi and tributaries). So, we also needn't build huge sets of centrally-planned infrastructure to enable the economy (although we have anyway, as a bonus).
Russia is on the opposite extreme: not much in the way of geographical barriers to invasion (open plains all the way to western Europe), so they must maintain a large standing army (and are chronically insecure and reactive). Russia also lacks useful waterways for connecting different parts of the country (most rivers flow north into the Arctic, others freeze for much of the year, etc.), so they must invest in considerable infrastructure just to enable the economy to function. These factors combine to push Russia towards a strongly centralized system (both politically and economically). That needn't be communism as such (the new oligarchism is similarly centralized), but it's hard to see how you can have communism without such centralization.
China is somewhere in the middle: some pretty useful rivers (though they require linkage via canal to truly connect the country), and decent geographical barriers to invasion (Himalays, deserts, ocean). To the extent that China feels insecure these days, it owes to the presence of much more powerful actors that could overcome those barriers without much trouble - historically China has been rather secure, even to the point of becoming blase about such. But I'd suggest that China's considerable demographic pressures may be more important that geography in terms of pressure for centralization.