Re: Why did spock end up in the alternate universe??
I already stated the easiest way for him to return to his original universe: Travel back to right before Nero arrived. Close the rift and/or blow up Nero's ship. This makes the 'new' timeline pretty much identical to the old one. Only difference would be that the Kelvin noted an electrical storm in space, but it quickly dissipated without an apparent cause. On to next adventure...
Now you're on the right timeline, and Spock knows a million ways to get back to his time. Slingshot, Guardian, etc. Only reason he didn't do this is because they didn't WANT to reset the timeline, they wanted it left alone for future movies. Not really any "in-universe" explanation that makes sense, they've fixed worse problems before.
Perhaps, if I am very lucky, the feeble efforts of my lifetime will someday be noticed and maybe, in some small way, they will be acknowledged as the greatest works of genius ever created by man. ~Jack Handey