As a native, I would write, "....no other sport has increased popularity over the last 30 years as quickly as basketball.
Technically, it is improper to end a sentence with a preposition. So you should never say, "... as basketball has."
Many Americans erroneously end sentences with prepositions. The most common example is, "Where are you at?" This is slang, and indicates a lack of education.
In your third example, the word "than" is not used properly.