The answer to your first and second questions would appear to lie in what Daniels said to Archer near the end of the first part of Storm Front...
ARCHER: "Who were they?"
DANIELS: "The most dangerous faction of the Cold War. They're led by Vosk, a fanatic, violently opposed to the Temporal Accords."
ARCHER: "Stay with me. Stay with me."
DANIELS: "We almost captured him, but he developed a form of stealth time travel. He escaped into the past. We eventually located him, but it was too late. He returned to my century. He and his people defeated us and launched this war that's destroying all of time. I've sent you to this point because it's here that Vosk can be stopped. If you succeed, the war will never happen. The timeline will be restored."
ARCHER: "One of his people told me they were building a conduit."
DANIELS: "Vosk's time travel device had a drawback. It was a one-way trip. He needed to construct the conduit to get home, but he was forced to use technology from this time period. The machine would have to be enormous. Find it. Destroy it. He must not succeed. Stop him."
According to his, if Vosk had succeeded in returning to the future in Storm Front, Part II, he would've escalated the Temporal Cold War into a full-scale Temporal War, resulting in multiple temporal incursions, one of which created the alternate version of WW2 we saw in those episodes. Killing Vosk before he could return to his own time prevented the war escalating, and all the temporal incursions that followed.
As to the identity of Lenin's assassin, I don't believe that was ever revealed. The only clue/s we have as to who that assassin might have been working for lie in the following conversation from Storm Front, Part II...
REED: "I think I've pinpointed where the timeline changed. Someone assassinated Lenin in 1916."
ARCHER: "Who took his place?"
REED: "No one. So without Lenin, the Bolsheviks never gained power. Russia didn't become Communist, and Germany never considered it a threat."
ARCHER: "Hitler was able to concentrate on the West."
REED: "After France, Belgium and the Netherlands fell. Hitler quickly took England and then the eastern United States."
T'POL: "But Vosk and his men arrived on Earth recently. A few years ago."
ARCHER: "Then they couldn't have been responsible for the changes that took place in 1916."
REED: "The police never captured Lenin's assassin. Some bystanders claimed that the killer vanished into thin air."
T'POL: "Daniels said that different factions in the Temporal War are changing history throughout the timeline. Maybe this assassin was working for one of them."
REED: "But I thought we were here to prevent Vosk from starting the temporal war."
ARCHER: "Chicken or the egg."
So according to this, the killer was not a member of Vosk's faction, the Na'kuhl, and was presumably working for one of the other factions involved in the Temporal War. As to which other faction, the claim that the killer "vanished into thin air" seems like a possible hint that the killer was Suliban, but we'll never know for sure.