The Roman world, at that time, was pretty big, and encompassed many more people than the Jews alone, so, Jesus was not just sent to the Jews. If what you say is true, then a South American who has put his/her trust in Jesus for salvation is a fool because the promise does not apply to him/her? And, nowadays, with all the intermarriage, esp. in North America, what's a person to do? What if you are European/Oriental or Oriental/African? YIIKES! What a mixup.
Re: Jesus being His own authority - only One who walked the earth could ever do that and that One is Jesus, because there is none higher than Him to be His authority, as He is God. God, of necessity, must be His own authority.