>Since property, both private and public, is a fundamental human right.

If property is a fundamental right, then shouldn't it be the right of a landlord to rent his property to whomever he wants?

Of course it should. But the landlord's private property is still a part of the country citizen's collective property.

Humans (and presumably human rights, if assuming they're fundamental) existed before countries. So how does a concept that came later (a country) suddenly trump something that's fundamental? What is the moral mechanism by which a group of people declare a certain area a country and suddenly gain property rights over everything within that area?

Human rights, just as countries, are a human invention. These inventions are extremely useful, because they allow some rules for conflict resolution — without them, it's just rule of power and violence.