This is a wide-ranging topic. Most of the questions you ask are traditionally answered by the idea of using private agencies (ie. Private police to provide protection, 3rd party insurance and arbitration agreements, etc).

However, without getting too deep into pointless hypothetical and trying to be as concise as possible I will say: The final outcome of a truly AnCap world will functionally look very similar to Small Gov / Libertarian world.

That is, in an AnCap world which is run by various insurance, standards testing, private police forces, etc....will practically not be a much different experience from say 1825 America with its 50 independent states model.

Therefore, we can achieve 90% of the same result, in an much easier to achieve format, by just pursuing a Small Gov / States Rights model.