Since these questions are already well answered in libertarian literature, I'll address each one with the respective sources for the answers.
  • Who enforces your natural rights?
  • If someone kills you on the street because you looked at them the wrong way, what happens?
  • If you enter into a consensual contract with someone and one party fails to uphold their end, who adjudicates?
Answers for these three questions:
Chapter "POLICE, COURTS, AND LAWS—ON THE MARKET" of "The Machinery of Freedom" by David Friedman (Milton Friedman's son)
This video is also a must-see; it's based on "The Machinery of Freedom": Link:
  • If a private individual dumps waste near your property, do you have the right to kill them?
No, lethal force is not a proportionate response to property damage or nuisance under libertarian ethics. Stephan Kinsella's concept of "Estoppel" provides a framework for understanding how punishment must be proportionate to the aggression committed. Here's his article about it:
  • And if they dump waste nearby, but it diminishes the value of your property and quality of life, what to do?
This scenario is known as a negative externality. This situation is addressed by the principle of negative externalities within libertarian theory. The affected party can seek remediation through private arbitration, where damages can be assessed and compensated, IF they have the right to do so. The right of compensation in the case of negative externalities is based on the homestead principle. In this article, you may find all your answers about how libertarian rights and also economic incentives work in this case.
  • If two individuals or groups claim ownership over the same piece of land, how is ownership determined and disputes resolved?
In libertarian ethics, there are only two legitimate ways to have ownership over a scarce resource: homesteading or voluntary exchange (agreement). So if the land was already being used by A when B arrived, then A is the rightful owner. If A and B try to claim ownership of the resource at the exact same time, then homesteading is impossible, so the only way is through an agreement, underpinned by the broader principles of non-aggression. This last part is not particularly explored in libertarian ethics because it is very improbable; however, it is a logical conclusion of libertarian ethics. Libertarian ethics are justified by Hoppe's Argumentation Ethics.
  • If a rival company engages in unfair competition by threatening or causing physical or economic harm, how should one investigate/intervene?
In a libertarian framework, other market participants and protection agencies would naturally counteract a company engaging in aggressive or harmful practices. The cost of such behavior would likely outweigh the benefits, as customers and business partners gravitate towards firms that contribute to a peaceful and prosperous order. The market's self-regulating nature discourages destructive competition and encourages businesses to maintain good practices to retain customer trust and loyalty. The company that engages in physical threats or economic harm would cost MORE for its customers while creating LESS peace and order. Why would the majority of people want to pay more for worse service when there are better options available?
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