Your battery will be fully covered because it's less then a year old. Nissan prorates their batteries according to age. Nissans oem batteries are pretty crappy though. Never gotten more then a few years out of them in any of my previous vehicles, including this Z.
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Take this for what its worth... When the first signs of the car hesitating to start due to a low battery, take it in immeadiately. The starting process repeatedly done will hurt the starter and then eventually that will have to be replaced too. Just my :twocents:

Took the car to the dealership this weekend and they did a load test, and everything came out fine. But the day before I went to the dealership I got some recording of what the start up of the car sound like, but they said they couldnt do anything, and I think they said that becuase they said the car wasn't doing it when they did the load test.

Another thing that I notice is that on a cold start the car starts up fine, and when I go somewhere and park it and let's say am at the store and 1 or 2 hour go by. When I go back to my car and start it up it's when it has a hard time starting.

This is the same issue I'm having with my brand new Z. She only has 3K on her. All of done to the car is install the GTR ignition button and installed new radio/speakers. Its kinda ridiculous! If anyone could help with this issue, it would be great. My dealer is over an hour away, so I would like to try to fix this on my own.

mine will want to stall if i drive it in the heat then stop and get back in real quick.

she doesnt like to start hot or right after you turn her off. :/