The metaphor here refers to an airplane leaving the ground.
I think the first sentence is just a typing mistake: ...has really become prosperous.
..become a hit is colloquial, but it expresses the meaning well.
"become prevailing" doesn't work. "...has prevailed over the competition" would be good English, but it's not what you set out to say.
...has been tremendously successful.
...is doing very well now.
...has become extremely popular.
...has attracted many customers and is doing a great volume of business.
Of course, there are many possibilities. Perhaps "become a hit" is the best. A cookie business is not really a formal situation, and the colloquialism seems to work here.