No, you don't "buy a star". That's a myth.
Try going down to the Hollywood Chamber of Commerce, offer them $30,000, and see if they will "sell" you a star. The answer is no, they definitely won't.
The Chamber of Commerce requires that fee for the upkeep of the sidewalk stars, but it is petty cash to the studios that usually put it up. It's an afterthought. And without fame, money alone won't buy you anything.
To get on the Walk of Fame you have to do three things. One, be famous - a household name in the entertainment field. Two, be nominated. (Anyone can nominate someone for a star, but sometimes people just neglect to do it.) And three, agree to appear in person when the star is unveiled (and schedule an appointment to do just that).
Many celebs have been awarded stars but then never got around to scheduling their unveiling ceremonies. And the stars aren't installed until they do. Paul McCartney, for instance, got a star ages ago, but just never scheduled a time to accept it.
As for Omar, either he hasn't been nominated, or he refused to show up in person to get it - because he would certainly be a a certainty to get one if he were nominated.