Set your goal to be to have fun -- not to be Habib Wahid
Like David said in the comments, It'll tae several years to get any good, regardless of when you start. If you start learning with the goal of playing Chopin, you will get discouraged. Instead, learn what is at your level -- and enjoy it. There's a lot of excellent music that you will play before you're able to play more advanced stuff, so don't give up on those experiences because you won't be able to jump to the difficult things that you have your heart set on.
I agree more or less with the timeline Todd set forward in his comment, although I would note that it depends very much on time invested, more with regularity than a few sessions of pure willpower and then weeks of nothing. The impressive thing about that pianist is not that he can play all of those notes quickly, but that he can play the notes quickly and well.
Playing by ear is entirely a learnable skill, and the best way to start is to be able to audiate (google it) and sing what you "hear," and then make the connection between the notes you hear and the muscles that push the right key on the piano. Learning solfege and stuff will help too, but the main thing is just to be intimate with your instrument and to practice doing it a lot. Help lead worship at church, find some people to jam with, all of those things will help improve your ear.
One last note -- Youtube is ok, but the very best is a private teacher. Even if you only splurge on lessons intermittently, having an expert to critique your technique (I make little rhyme, no?) will be a huge asset to your playing.
HAVE FUN THO