Need to understand where you are coming from on this. How does the state reinforce your natural rights today? It doesn't mine. It has a chance to use its force to coerce restitution for a natural right violated by another, if I can afford a lawyer. If I want to assert my natural rights, that is up to me whether there is a state or not.

You die, in all systems. Your family may seek 'justice' by asking the government to kill the person who did it, or put them in a cage. Without a state, traditionally situations like that were adjudicated by 'judges' who were wise and trusted elders that many families used for advice on disputes. Most families / tribes would agree that a judge's decision was final, though appeal processes would also exist. Look up weregild, that's just one of many historical examples.

In modern times, without a state, there would be those insured and those uninsured, those with pre-existing arrangements for how disputes will be settled, and those without. Localities would have traditions ('precedents') for how the 'without' would be treated in 'courts'. The modern court system would be a model that is used in almost all localities, and any locality that used something much different would be laughed at or avoided or revered with a cult following. It's just that they would be more accountable to the families/tribes they adjudicated for, the lawyers and judges would be more intimate and well known, and there would be less room for corruption. It would not be perfect, and doesn't have to be to be advocated for.

See above, depends on your pre-existing contracts. With a state, it is implied that the state will adjudicate. Without a state, your contract will specify.

No. But reality dictates they are more likely to be killed, or sued, than the average person, making such irresponsibility more risky than behaving ethically.

Keep in mind that these situations are almost entirely ignored/unaddressed by modern governments. If one spends millions on lawyering to try and sue a corporation or government for damages, one might get that corporation to pay a sum that does not come close to their profits, isn't likely to change their behavior, and may not compensate for the actual damage. That is what we are trying to improve upon.

Without a state, judges would be accountable to more than just elections with paper ballots conducted on machines that are easily hackable made by companies easily captured by intelligence agencies, for instance. Lawyers would be cheaper because competition would be greater, universities wouldn't be elite institutions propped up by government grants, but easily accessible to all, and the system would be more efficient, for instance.

See above. It's simple when you recognize that courts can be voluntary.

Corporations that don't abide by cultural standards and norms and don't carry insurance / adjudication contracts with courts that are popular, recognizable and with a reputation of avoiding / addressing such things when they occur will not be the ones chosen by individuals in the market. They will be seen as much more risky. Getting caught in unfair competition, in the status quo, has no repercussions, and is in fact rewarded by government. That's what we're trying to improve upon - total chaos and unaccountability and corruption in exactly the areas you are concerned about exists right now. Any system would be better than what we have. A stateless system is just one of them.

BTW, you forgot who will build the roads?