How to buy a new iPhone 5 online and I can get an 'Apple Care Plan' for it?

I'm thinking to buy a brand new Apple iPhone 5. I was told if I buy one from eBay, Apple will not recognize the receipt date and hence will not sell an 'Apple Care Plan' for it. I checked Walmart.com, Target.com and Amazon.com as an authorized seller; yet most of them only sell certified refurbished iPhone 5 units. =( Below are my questions…

1. How may I buy a brand new iPhone 5 and still can get an 'Apple Care Plan' for it?

2. How may I buy a valid 'Apple Care Plan' on eBay or online for a brand new iPhone 5?

3. Does it mean that iPhones marked as "Factory Unlocked" only use GSM Sim cards?
and cellphone service carriers, like Boost, do NOT use GSM Sim cards?

4. Does Boost have a good coverage in New York City?

5. What other cellphone service carriers provide rates as low as Boost?

~Merci beaucoup for your sharing!

Well the thing is that the iPhone 5 has been discontinued for almost 4 years, so you won't be able to buy Apple care for it.

Boost Mobile runs off of Sprint's cell towers. Sprint is extremely hesitant, and I mean extremely, about allowing non-Sprint phones on their network. I don't think you can officially add a non-Sprint or Boost phone on Boost network. It may be possible, but it may not be that easy. Even though Sprint/Boost is a CDMA carrier, they still use SIM cards for 4G data.

The phone is not guaranteed to work with Boost. You are free to try, but just be prepared for it not to work.

I don't live in NYC, so I don't know how well the service is there.

You have to buy the phone BRAND NEW to get get the basic Apple Care warranty and yes it has to be new to get the Apple Care Plus warranty as well. The ONLY place you can buy a refurbished iPhone and still get basic or paid warranty is directly from Apple.