Was the display of a religious icon, a result of a judge enforcing a law?
In Moore's case no, in fact he had to bring the monument in at night, in secret because he knew he couldn't get away with it if he did it openly. There have been attempts to pass laws to force schools to put up specific christian materials, but they are unconstitutional of course.
Will the judge have to quit his religion because he is a representitive of government? Or does having a Christian judge offend people and violate the Constitution?
A person is allowed to believe anything they want. It only can be a problem when they try and force that belief on other people. For instance, a judge is allowed to pray before starting court, but he is not allowed to lead the court as a whole in prayer.
Also I ask is displaying a religious icon imposing religion on the population?
That depends on several things, including your intent in displaying the item, if other items are allowed to be displayed, where the item is being displayed, and who is paying for the display.
To give a more concrete example, imagine that some new religion has swept across the US so that 51% of the population follows this religon. This religion requires that all members pass through religious sin arches at least once a day.
For the government to spend tax money to put sin arches in front of government buildings would unconstitutional. For the government to allow private groups to build sin arches on government property would generally be unconstitutional. But it could be allowed in special cases if the arches are placed such that people that don't follow that religion don't have to go out of their way to avoid the arch.* A judge that wants to put a sin arch in his private chambers would generally be OK, as long as it wasn't placed such that everybody going into and out of the chambers had to pass through the arch.
* The reason for this is that the government is required to allow the free exercise of religon. But the government can not support that exercise. Balancing those two things against each other, and balancing free exercise against harm in cases of dangerous religious practices is a very complex and situational question.