The Enterprise that was built in the prime universe, would still had been built in JJ. alternate universe. It would still have been built and launch in the same time period as it was in the prime universe. It would had the same registry number as the prime universe Enterprise and still would been a Constitution class starship.
Because George Kirk had die when the USS. Kelvin was destroyed? He wasn't there to save the Enterprise from being destroy.
No. The "prime" Enterprise 1701 was built, supposedly, in 2245--that is AFTER the Narada incursion, so there is nothing to require that it be built in the alternate timeline.