As I use the phrases, here are the differences:
If you fake someone out, you do something that makes them think you are going to do X, when you are actually going to do Y.
I thought you were going to drive to the basket. When you pulled up
suddenly and took that 10 foot jump shot, you really faked me out.
When you fool someone, you get them to believe something which isn't true, and it usually is not serious but some kind of joke.
Dressed up like that, you looked like an old man. You really fooled me
with that mustache and the gray wig.
When you deceive someone, you do something or say something that causes them to put their trust in you, and then you betray that trust in some (serious) way.
He told her he was going away on a three-day business trip, but he deceived her. He was actually getting back together with his ex-girlfriend.
Other speakers may use these terms differently.