The sentences are correct, except #1 should be: I have no family besides my parents. If it helps, for all the sentences you could replace "besides" with "other than." So you could also say: 1. I have no family other than my parents. 2. No one, other than me, has worked it out yet. It's not any better, just equally correct. You can also replace "besides" with "outside of" -- a little awkward but still technically correct. "Besides" just separates that part of the phrase from the rest of the sentence. "I have no family" isn't really true. You have parents. Someone HAS worked it out. The third phrase is emphasizing that the sentence is true even if you take out the most obvious commonality (music) or quality (being beautiful). Alternate ways to say the first two sentences: 1. My parents are my only family. 2. I'm the only one who has worked it out. - or -- No one else has worked it out yet.

Those are all correct. The phrase "I've got" I think follows grammar rules, but it's just very casual/informal. So you might hear it said, but I probably wouldn't write it. I'd write "I have no family besides my parents." or "I have only my parents as family." I never realized how confusing this was until I tried to explain it!!