Can A Website Be Fake

Yes. Some types of "fake" sites are not fake, but simply scams.
Example: pspblender.com The site does provide what is promised, but in a fraudulent way. It only searches torrent sites for "psp" and shows you the results. Other websites deemed "fake" are websites for phising. "Phishing" is when one attempts to steal another persons' personal information, such as account names, passwords, and social security numbers.
These websites often disguise themselves as other websites, for scam example, Facebook, in order to deceive the user and make them believe that they are on the official site, where it would be safe to log in, but it is not, as they would actually be sending information to another server altogether, where somebody will receive the real information and be able to use it on the real website.

I could go on, but I won't.