It will have full 1 year Warranty with Apple from the time you purchase it. When you get it you can check the Serial # with
just to be certain.
Not likely... it's a refurb. Most refurb's offered by the carriers only have the warranty offered by the carrier.
Only refurbs sold directly through Apple come with the 90 day warranty.
Read this on a Sprint forum:
If the customer purchases the device through a service provider, then the device will have to be re-registered with the correct date of purchase. This will have to be done through Apple support or through Apple Care if support is unable to correct it. They will in turn get the 90 day phone support and 1 year hardware warranty. If purchased through 3rd party sites (i.e. Amazon, Ebay, etc.)they do not get the warranty or phone support.