To be another Bill Gates you will have to have a ridiculous amount of luck, just like he did (be born rich, be one of the youngest people in the world with access to a timesharing system, and have IBM hand over the most lucrative part of their business to you).
To be an expert programmer probably takes about as long as becoming an expert in any other field of similar depth. At least 4 years, but probably more like 8. Unfortunately, anyone who can write a working program thinks they're an expert.
As for how much to study a day ... that's just idiotic. If you enjoy it you will do it. If you don't enjoy it, do something else.
Well, actually, Bill Gates was somewhat of a decent programmer in his time. He wrote an implementation of BASIC for IBM (or something like that. I remember being moderately impressed), IIRC. But he didn't become a billionaire by writing code, I can tell you that. The same goes for Steve Jobs.
If you get into a computer-related career, particularly computer science, do it because you like it. If you do it expecting to make obscene quantities of money, you'll become a) mediocre and b) disappointed.
If you just want to make money, a business "career" might be more appropriate.