First question, some people do believe that. They are the ones that are referred to as Christian Nationalists in the link. Others call them Christofascists. They violate the first amendment by imposing their beliefs as law for everyone to follow.
Second question - It is not the place of politicians to tell churches and other faith organizations what spiritual path to follow or how to follow it. That also violates the first amendment.
Third question - No, he didn't. Regarding Roman government, he said, "Render unto Caesar the things that are Caesar's, and unto God the things that are God's."
Regarding the Jewish establishment, he preached in synagogues as well as in the countryside to crowds of people, which was within the custom of the times. He discussed and interpreted Jewish law, as did many rabbis at the time. There were numerous sects within Judaism at the time. He overturned the tables of the money changers because they were using the temple for business profits instead of respecting it as a spiritual place of worship. That was a religious move to condemn religious abuses of the people and the temple.
Last question, the part following the words "or did he" - You have reversed the order of events. The ride into Jerusalem happened first, then the scene in the temple a few days later. The donkey was a symbol that people of the times, versed in the teachings about Judaism, would recognize. It symbolized being a spiritual leader of religious reform, not the militant messiah (annointed one) that some sects of the times were expecting.