Regarding the motorbike, I can see how it fits into NuTrek. In ST09 we saw Kirk in a hotrod and on a bike (a different bike; the bike in the trailer seems like an older type). And going on a five-year mission, crew are probably entitled to bring some personal items to keep them sane on the journey. Kirk brings along his bike, for sentimental reasons. Spock might bring along his Vulcan lyre.
I can imagine McCoy ribbing him about the bike - "What century are you from? It's a piece of junk!"
Then, when they are on the planet, Kirk recovers the bike from the wreckage. He turns up on it to rescue McCoy, and gives him that ironic look that is classic Kirk. "Need a ride?"