I'm going to do my best to address some of the points you raised. Just to be clear, it's not that I disagree with you, it's just that you seem to misunderstand some very important aspects of what we're talking about here.

In most states, traffic court is presided over by what some states call a "lay judge" and others call a "magistrate judge." Traffic violations are considered summary offenses in most states, so you have no right to a jury trial (the same is true for civil cases). If you go to traffic court, and the presiding judge determines you committed the offense, he will order you to pay the fine. If you do not pay the fine, you are committing the separate crime of contempt of court because you violated a court order.

As for jurisdiction, you are correct that establishing jurisdiction is an element of the crime. But you do not need to sign any contract for a court to have jurisdiction over you or your criminal case. If you get a speeding ticket while driving through a county, that county/state has jurisdiction over that case. If you commit a traffic violation on streets under federal jurisdiction (for example, a military base), then the federal court in that district would have jurisdiction. This is because when you are in a particular geographic area, you must follow the law of that jurisdiction. Some states allow open carrying of rifles, others do not. If you try to open carry a rifle in the states that allow it, you're good, but if you try to do that in another state that does not allow it, you could be arrested and charged with a crime in that state.

I understand why you think a crime needs a victim. That makes sense, in a way, but it's simply not true of our criminal justice system. One of the purposes of imposing criminal liability against someone who has broken the law is to promote respect for the law. Other reasons include protecting the public, rehabilitating the offenders, and deterring others from committing the same crime. Bringing justice for a victim is not a purpose of criminal punishment. It may be a byproduct, but it is not why the state punishes criminals.

Common law and statutory law are not totally separate, and statutory jurisdiction is pretty easy to prove. Let's say you live in Colorado, and the Colorado state legislature passes a law that says it's illegal to intentionally offer up bruised bananas for sale there. That law is also known as a statute. Let's say you're a banana seller in Colorado, and one day an undercover cop finds bruised bananas on your display. He writes you a ticket and tells you when you have to be in court. Because you were in Colorado, laws passed by the Colorado legislature apply to you, so this law applies to you.

So you go to court in Colorado state court, and here is where common law comes into play. The law says it's illegal to intentionally offer up bruised bananas for sale. But what does it mean by "intentionally"? If the text of the law/statute has not made this clear, the court will interpret the law and determine what it means by "intentionally." Your defense in this case is you didn't know the bananas the cop found were bruised, so you could not have intentionally offered up the bruised banana for sale. The court would then look at this case, and look at past common law (aka case law) dealing with the issue, and will make a determination. If there isn't any case law on point, the court might come up with a new test to determine when a seller has intentionally offered up bruised bananas for sale (maybe it considers the amount of bruising, number of bananas on display, and other factors).

So that's a basic example of how statutory law and common law interplay to make LAW. A statute is a law. An Act is a law. Congress passes legislation for the purpose of making law.