No doubt in my mind it's fake, you just simply can't source genuine apple products through Chinese manufacturers, in fact if you call Apple themselves, I'm sure they will be happy to tell you the same thing.
Quick question, what site did you buy your phone from and how did you pay for it?
I hope it's not the site you have mentioned above. I wouldn't go near that site myself. If they aren't scammers, which I believe they most probably are, the products are fake.
The hotmail account is a good indicator of a fraud site, without taking absolutely anything else into consideration.
You can do a WHOIS check, try typing their name into Google with the word fraud or scam, see what you get.
If you want to stay away from scams and fakes, you really do need to stay clear of Chinese suppliers if you are going to buy branded products.