This isn't the Spock from the original universe. This is a character who's had some different experiences, whose planet and culture may be slightly different from the original series, and whose personality seems to be more openly emotional. He isn't going to react like the original Spock and I'm just fine with that. Let them do something different with this alternate universe. It's glaringly obvious that Spock and Uhura are having sex, have been in a relationship for some time, and are very serious about each other. Uhura was not just comforting her "good friend" in that scene. She was comforting her lover and he was seeking comfort from her.
You know, comments like this sort of undermine the idea that this is the exact same timeline, just changed a little. Nothing that changed should have had any effect whatsoever on Spock, until after the Narada showed up in Vulcan's orbit. If you want to claim that Spock was already having a relationship with Uhura before that, then you can't really claim that this is also the original timeline that's just branched off at a point; either Spock is Spock until something different actually happens, or Spock is not Spock from the start.
Not necessarily. In the original timeline, Kirk had attended Starfleet Academy years earlier than in this timeline. His presence (or lack of it) at the academy at an earlier point may have altered events as they played out in the new timeline. He might have gotten to Uhura earlier, or somehow interfered in the development of a Spock/Uhura relationship before it happened.