Don't look mysterious, don't stare at airport security, DO NOT TAKE PHOTOS IN AND AROUND AIRPORTS, act calm and civil, obey customs officers unquestioningly. Essentially until you're out of the airport just follow signs and follow instructions, opening your mouth is not required. When you give your passport to the customs officer, they will ask some questions which you should answer with short, clear answers. Don't lie, don't launch into a vitriol of useless grandmother stories. Also don't be nervous, they won't eat you.
When you transit be sure to check in for the transit flight immediately after you land. Don't delay or you'll regret it. Other than that just try to get as much sleep as you can on the plane because you'll need to be alert in LA and Taipei airports, both are very crowded airports so you'll need to be alert.
Anything else you specifically want to know? Enjoy listening to country music