Mine had a couple hour charge on it, but it was delivered directly from the factory. If you bought it in store it may well have been sitting in inventory for a couple weeks and trickled charge out. See how it fares after a charge or two.
They do but majority of devices turn on straight out of the box. In the OP's case, I think this unit's just been sitting in shelves. Did you purchase from a third party? I wouldn't worry too much about it since it's new and comes with warranty.
Sometimes if it gets shipped in the cold the battery will drain. I don't think it's a problem. You have 14 days so just make sure all the ports are working, the battery is lasting for about 8-9 hours, it isn't crashing, etc.
If it passes all that and doesn't freeze up or anything you're set.