You are wrong regarding anarchy. I never said we should have no laws, I said we should not have laws that prosecute people that have done nothing to infringe on the rights of another. Big difference.
So you're fine with "armed government agents" in principle. That was the point, that your line about "armed government agents" is overly emotional hyperbole. All laws, in the end, rely on "armed government agents" to enforce them. Therefore, if you're decrying "armed government agents", you're announcing your opposition to any sort of law.
Inflated prices arising from a monopoly over a particular resource inevitably results in alternatives and technological advances that renders the monopoly moot. More importantly, no one is forced to buy from the monopoly. You can always go without that resource, You can always walk away.
No. Not how the real world works.
Healthcare. We have near-monopolies. Prices are incredibly inflated, compared to nations where government takes a more active role. And essentially everyone has to buy.
Internet. I have a choice of _one_ very expensive broadband provider (satellite internet, being even more expensive, is not an option). No new players are entering the market. Forgoing internet is not an option. Nations where the government takes a more active role have much cheaper and faster internet.
In both of those cases, the free market stinks compared to the government.