Can a State Body be the plantiff in a civil case?

It happens all the time. The town is like a corporate entity in many ways, including the right to sue or be sued in court. My town recently sued a taxpayer, in superior court of the county, for violation of the zoning code because we have no administrative procedures to handle it in town. In another scenario the town could sue a person in civil court for damaging or stealing town property.

Another common "state body" is a public school or other institution, which may enforce its own rights in civil suits. For example, a state university may have valuable trademarks or other property rights that can be protected by suing an infringer in federal court. (think "GATORade")

If "public offense" is intended to mean "criminal violation", then the question of civil suit in addition to criminal charges would depend upon whether the law also provides a civil remedy for that crime. If the violation were one of the "victimless crimes", then it may be difficult to measure damages, even if there were a civil cause of action.

Why, yes. Of course.

Of course. Happens all the time....

Take child support cases for example...They are civil suits brought against "civilians" in civil courts....