"it's" is a contraction of "it is." Without the apostrophe ( ' ), "its" is a possessive pronoun, meaning "belonging to it." I would really like to see more of the context to answer the second question, but with the information provided, I will say that "ones" is used like a pronoun to avoid repeating "stars" and "good" is and adjective modifying "ones." Restated, that quote could read "The stars it is really one of God's good stars." However, that is why I'd like to see more context. The sentence as it is doesn't make a lot of sense. If there were another sentence, or even a phrase, preceding that quote, it could make a big difference.

I think it should be "The stars...it's really one of God's good ones." The person wanted to say "good ones" which is singular, so I think she was treating the stars a a singular object. "good ones" means one of his creations. It actually means "The creation of the stars, it's really one of God's good ones."