how is obedience to authority relevant in Romeo & Juliet? Which characters are rebellious? what punishments do they recieve?

Both simply fall in love and refuse to listen to anybody. They only act on impulse listening to their heart or rather loins. They are both rebellious and their ultimate punishment is their death.

I suppose they had individual punishments too. Juliet was forced to listen to her father and Marry Paris right away. Ro meo was banished to Mantua because he finally felt like a "man" and killed Tybalt.

There is disobedience on every level of Verona's hierarchy. The prince is not a good leader because he changes his mind about punishing people who are caught fighting. As a result, lots of people end up dead. Tybalt doesn't listen to his uncle and challenges Romeo to a dual. Juliet disobeys her parents, the nurse disobeys her employers, and the Friar, while arguably well-intentioned, lies when he is expected to be honest. In Shakespeare, whenever there is a leader (prince, king, father, etc.) who changes his mind that is a sign that he is a weak leader. Juliet calls Romeo "the god of my idolatry" which could be a sign that she's not worshipping the right being; she should not be worshipping Romeo, and the Elizabethan audience would have found this line very telling.