Nelly has a (bill)ion dollars worth of jewelery in his mouth. The reference to Hillary Rodham Clinton, who is married to Bill Clinton implies that Hillary would perform fellatio on Bill, having "Bill" in her mouth.
when i exhale, my breath will move past my diamond-studded mouthpiece (or "grill"). diamonds are also called "ice" (they both sparkle), so he is jokingly saying this will change the weather (cause a cold front, because the ice would make his breath cold).
if you have a very curvy body with large breasts and rear end (emphasized by "thicky thicky thick"), you can approach me with confidence to ask for a ride in my car, ask me to buy you a drink at the club, or go home with me for a romantic encounter.
George Foreman sells grills that cook while eliminating a great deal of fat from meats. this is comparing his success to selling a different type of grill - a shiny mouth piece covered in precious stones/metals that you wear to be fashionable and show off
while you're spending time with a lady, if she ever acts as if you are a couple (says "let's go back to our house" or "let's get in our car" etc.), things have gone too far and you must get rid of her before she wants a serious relationship or your money.