No, they never existed to go back to the '30s.
Yes, they did.
Remember, the divergence only happens in 2233. Any time before that, there is only one timeline, not two.
Time travelers from either the prime or Abrams timelines can travel back to any point prior to 2233, and while they're doing that, they can even meet. They're simply two possible futures. Either one is equally real.
No, that's not how alternate timelines work. The divergent point was in 2233 but the fact that an alternate timeline was created makes them both separate from each other in all aspects. Therefore while both timelines' pasts would be identical up to 2233, they're still completely separate and they don't overlap. If they did, all that prime-Spock would have to do to go home is slingshot around a sun to 1930, go to Earth, wait for his younger self and co. to show up and then go back to through the Guardian with them and then take a second hop back to his own future.

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