Is my iPhone fake?

You are addressing this to another user and not to Apple in this forum.

Apple Support Community Forum

This is Apple Support Community forum, primarily for a user to user interaction for information & idea sharing between users, if need be, extend support on technical know-how in handling Apple products from a more experienced fellow user, This is not the right forum to discuss with Apple Inc.

Take your serial number and go here -> Check Your Service and Support Coverage - Apple Support

I believe F2 at the beginning means assembled by Foxconn. Other than that you can look it up by entering the entire serial number.