If I recall properly, our Lord Jesus told them they had made "His Father's house" a den of thieves. Since the house belong to His Father, I would say He had authority over it.
You can't "obey" authority without defining it--as Romans 13 clearly does. Unless you want to call God a liar (do you?)
And how is it defined? I believe I have stated many times now that the commentators all agree that Paul is talking about obeying government bodies. There is no need to say that God is a liar. He is rather clear on the subject.
someone who is not a "rewarder of those who do good" is not in authority.
I would call to your attention Pilate who was given the authority to execute our Lord Jesus by God. At least that is what our Lord stated.