Am I International?

Yes for some UC schools and most CSU schools. But for the competitive colleges like UCB and UCLA, the requirement is different. UCLA requirement is slightly higher than UCB.

https://www.admission.ucla.edu/prospect/intl.htm

Some schools require TOEFL scores so that they can identify your listening and speaking skills. The SAT does not provide that kind of information. I know an international kids who attended US boarding schools in 4 years but his TOEFL speaking score was low.

Take the TOEFL if you can. If you have high scores, submit them.