A is the closest to being correct.
There is no "general" trial judge. A judge may sit on a trial court but they are not a "general" judge. They may be a State judge or a federal judge on a court of original jurisdiction.
There are administrative judges at the patent office, so that is correct.
The idea is known as the Republican form. The idea is that people democratically elect those who would represent them in a government, and those people would be held accountable for what they've done if they do something opposite to the will of the people. It's the only way that a democracy can work properly because others would be impossible with that many people.