What criminal and civil courts would look like under libertarianism (taking into account that the state is assigned only the role of enforcing court decisions)?

Anonymous question

Everything is simple with civil courts: commercial arbitration already looks the way civil courts should look under libertarianism. The parties agree on whom to invite to adjudicate, that person adjudicates, and then the parties execute the decision. Whoever refuses bears reputational costs, and in a minarchist state, it wouldn’t end there; the state would send bailiffs to enforce the arbitration decision.

With criminal law, it is slightly more complicated.

When the person who used violence does not hide, the task is reduced to the previous one: they and the representatives of the victimized party agree on who will judge, then the court’s decision is executed—voluntarily or forcibly.
If the person who used violence is unknown, first the party interested in the investigation either investigates the matter independently or hires detectives, and only after the NAP violator is found, there may follow either a trial or retribution.

A court cannot be imposed on anyone, because a court decision whose jurisdiction is not recognized by all litigating parties is legally null and void. But if instead of a court, retribution simply took place, then the party that carried out the retribution will now have to prove itself that this was not a violation of the NAP. They will litigate with those who are ready to condemn them for the retribution, present the collected evidence of the NAP violation by the victim of the retribution in court, and will be acquitted. Or not, if the evidence proved insufficient.

Thus, if a criminal hiding from justice realizes that they are already breathing down their neck, they are extremely interested in reaching the nearest prison in time and buying refuge from retribution there while negotiations regarding a trial are underway.

And if you are in prison voluntarily, you would prefer to rent a comfortable room

Which industries/spheres will remain in the hands of the state in the Libertarian Russia of the Future? Or will everything be private?

Anonymous question

The question itself already contains part of the answer. Since we are talking specifically about a Libertarian Russia, this already implies a minarchist scenario. Within this scenario, diplomacy, the protection of citizens from external aggression, and the enforcement of court decisions remain in the hands of the state.

Why diplomacy is the easiest to explain. If there are states in the world, it means there can be interstate agreements, and therefore it is necessary to maintain a certain state structure that will prepare and sign these agreements.

In a similar way, one can understand why the protection of citizens from external aggression becomes a matter for the state. It is easy and pleasant when external aggression is carried out by some bandits who are not part of the privileged club of state bandits. A private company can handle them without any diplomatic consequences. However, it would be difficult for a private company to explain to someone like Kim Jong Un that he is wrong: to him, they would look like some terrorists with whom negotiations cannot be conducted, if only because there is no one to talk to: the state considers only another state as a counterpart.

The most questionable justification is why the state should be allowed into the sphere of enforcing court decisions. But even here, one can refer to possible incidents with foreign companies, who might perceive violence against them by private actors as lawlessness and run to complain to their own government.

In any case, this is how minarchists envision the desired future, and I, generally, am not against it — but only until non-state practices begin to be actively implemented in these three areas as well.