Things about libertarianism I don't understand

[Tiberius]

Libertarians posit that everyone has an absolute right to life and the property they own. Any instance of infringing on these two rights is wrong.

Agreed.

Libertarians generally describe government as a "necessary evil" that protects these rights. Under this view, libertarians think that a land with no government is ideal but that the free market wouldn't be reliable enough to secure the rights of its people. So, libertarians allow the existence of government only to have control over the justice and protection of its citizens and perhaps for handling public transportation. Everything government does is still "evil" but it's allowed because it's the only practical alternative. However, the completely "free" society free of government is still the ideal thus government should be as small as it practically can be.

This is where I disagree. Not everything the government does is evil, and Libertarianism requires the existence of a government, otherwise it would not be distinguishable from anarchism. Indeed, a small government which does not interfere with the lives of law-abiding citizens is an example of a good Libertarian government. There is nothing evil with upholding rights and protecting citizens from abusers of those rights.

One should not confuse Libertarianism with free-market capitalism. The two are different. Libertarianism is a political philosophy; free-market capitalism is an economic model. Libertarianism supports free-market capitalism as an economic model, but the free market has nothing to do with upholding the rights of citizens...it only describes how ownership works and how people can trade.

This distinction however between government and the "free market" seems to me to be an artificial distinction. If goverment is monopolistic control over justice and protection over a certain area, then any property owner, any business, any HOA etc in the hypothetical completely free market scenario is a goverment. But libertarians have no problem in principal with for instance an aparment complex owner establishing rules for how it's occupants can behave. There's nothing "evil" about apartment managers.

What's the essential difference aside from size between government and an apartment manager?

It's not an artificial distinction, as I've described above. You are wrong to say that a Libertarian would have no problem in principle with an apartment complex manager establishing rules for how occupants can behave. Whilst we would say that rules for the apartment complex are largely set by the manager, there are certain rules they cannot implement; for instance any that contradict those set by government, or which infringe upon the resident's rights. A Libertarian would not be fine with an apartment complex manager allowing people to keep slaves for instance.

Libertarians also hold that contract and contractual law is very important. An apartment complex owner cannot just change the rules of the apartment unless this is in the contract that the residents signed.

As far as I can tell, most Western democracies aren't infringing on libertarian's rights. A modern Western country such as the US, is just basically an enormous HOA governed neighborhood. If "wrong" is infringing on your right to self or property, there's nothing truly wrong with say government restricting the lightbulbs you can buy, banning guns, taking your home away to build a freeway, etc., because you never truly had an absolute right to self and property in the first place. You gave that up by virtue of being in the country. These are no different than the HOA saying you can't paint your house orange, or the apartment manager saying you can't have pets.

The point about rights in Libertarianism is that they are natural, and cannot just be overridden by any government. Rights are above laws. Laws exist only to uphold rights. This is a central belief of Libertarianism; that rights exist a priori. People can give up their rights, sure, but that doesn't mean they stop existing. Generally when talking in terms of countries, people are forced into giving up their rights by the government.