Decide if the following sentence is grammatically correct or incorrect. algunas personas quieren ser famosas.

Yes, this sentence is grammatically correct.
The sentence translates as 'Some people want to be famous.' Since the word persona is feminine, this means that the pronoun next to it (alguna) also has to be feminine, which here it is, and the adjective famosa is also feminine. Since the word personas is plural, the pronoun algunas has to be plural as well (which it is), but also the verb quieren has to be plural (which it is), and the adjective famosas has to be plural (which it is). So, the sentence is correct as it is.

Los exploradores quieren  descubrir  nuevos mundos.

The only change would be to add the accent on esta (on the a) in esta in number 15.