Ending question

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Yes, that was the implecation.

Yep. There's the part where you strangle Dragovich, and Mason says "You tried to make me kill my own president!" to which Dragovich laughs and replies "Tried?!" Then there's the intel you can collect which I think suggested the CIA was going to terminate Mason, which obviously they didn't. There's also the ending cutscene with Mason in the crowd at Dallas, Texas, and he mentions "Agent Oswald compromised," then he mentions a bullet caliber suggesting he was one of the supposed shooters.

Interestingly Oswald did live in the USSR at one point, and returned to the US. At one point before the JFK assassination Oswald attempted to return to the USSR through Cuba, but the KGB in Havana recognized his name and prevented him from leaving the US. Plus the way Mason talks during the cutscene makes him sound almost hypnotized. In BO2 some US Army soldier asks Mason if the Soviets really tried to brainwash him, which Mason responds "They gave it their best shot." It seems like Mason was indeed successfully turned into a KGB sleeper cell and killed Kennedy, but doesn't remember it and thus assumes that Dragovich failed.

If you ever read up on Manchurian Candidate conspiracy theories and sleeper cells, some people who claim to have been recruited claim that they have gaps in their memory or that they can't remember doing things. Oswald himself claimed he was a patsy, and the guy Sirhan Sirhan who shot RFK also claims he didn't remember doing it. Read up on some CIA projects like Project ARTICHOKE, personally I think it's legit but when it comes to JFK I don't think it was the Soviets, I'm pretty sure it was LBJ.

Can't be too careful with all those weirdos running around.