How to check which country the iphone comes from ? How to check iphone is original or not ?

What is the model number of your iPhone? Settings>General>About>Model.

You may have to scroll to see the entry for Model.

Does iTunes recognize the iPhone when you connect the iPhone to a computer?

fake iPhones does not run ios so they don't work with app store or iTunes or...

Just go this page https://checkcoverage.apple.com/ and enter the serial no. of your Apple product and the page will show you about warranty and details about your apple product. From this page you can confirm about whether your product is genuine or not.