I like Natasha hero unit personally. While she won't cause as much mayhem as Tanya or Yuriko in the middle of enemy base, she has great range to compensate. I'd rather have a commando take out few key units/structures out from a safe distance rather than have them up close and at high risk of dying. Raw power-wise though Yuriko ftw.
The best way I can think of to describe the time travel is it's timelines. There was no Hitler, ever, in either timeline we see. Einstein did that already, and when someone is removed from the timeline they're *removed*, not just from then but entirely. In the 'original' there was no young painter named Adolf. So when the soviets went back, now in this timeline there never was a Hitler, and there never was an Einstein. (Future Tech are the ones who in turn come up with all the cool tech Hitler did like the chronosphere, and time travel. It's implied they're run by time travellers too...) As for how the Empire invaded from the west... uh... time travel teleport shenanigans! :D It's like when you wonder how the USSR invaded the USA from the *east* coast in the second game I guess?