The words "up to" have one meaning together as a preposition. See definition 3 here: http://www.collinsdictionary.com/dictionary/english/up-to The words modify the rest of the phrase, which is in fact all the words after "up to", in the sentence.

Neither. It's a preposition. The prepositional phrase "up to twenty times..." modifies "star".

"Up" can be an adverb, an adjective, a noun, and a preposition. In this sentence, I think it's an adverb.