I think it's pretty safe to say that the intelligence agencies of almost all Cold War era allies are still close partners. Governments on either side still generally regard the other side as potential adversaries.
Of course, the Swedes still officially claim to be neutral, like they were during the Cold War (and in WW2 and WW1). In practice, it's of course obvious which side they liked best.
I don't think it's nearly as clear cut as that. Neutrality means you're willing to work with whoever wins. It requires a high level of moral ambivalence.
If you are actively aiding one side or the other (or both), I don't think that counts as being neutral (if it does, it is certainly a very weak form of neutrality). Which is exactly what Sweden has done and is doing, dating back to at least WW2.
Sure, but just as the "democratic" side of the Korean conflict isn't the side of the Korea with "Democratic" in the name, the same is true of the "socialist" side of the Cold War.
Leninist (and Stalinist, etc.) states, of course, liked to put "socialist" and/or "democratic" in their names, but the entire Leninist concept of party vanguardism is intrinsically both anti-democratic and anti-socialist.
