This email is trying (poorly) to look like it is from Apple, you know Apple did not send it, yet you wonder if it's fake?
A real apple purchase email (for a product actually available in the app store) will show your apple ID, order ID, not offer to refund you immediately (presuming you have to give some kind of financial info to get this "refund" lol), not have massive spelling errors, come from an apple dot com address, so on