When we talk about rights, what rights are we talking about?
Am I to presume the Universal Declaration of Human Rights?
If so that's ok.
It covers rape, pedophiles raping children and murder; you're right, the owned property would be protected by what ever means the owner saw as necessary to protect the environment.
Unfortunately some of the things that aren't covered by this are children consenting to sex to whom ever they please, now that may seem all well and good but let us not forget the use of verbal coercion and duress.
This would also allow for child solders providing they gave consent.
Does a parent hold dominion over there child? according the human rights, No, the child would have to make decisions for it's self and there for would be held responsible for it's decisions (witch would allow for consent to anything accept slavery).
The parent will be in control of them for the most part because the child is unlikely to separate from there parents control early on, unless the child them self say what they want to do something and no one has the right to interfere with that in accordance to the UDHR or face punishment that may include death.
The laws that prevent things like this are subject to the country and not included in the UDHR.
So now let us consider that if one were to stop any one from engaging in any of these the Rights™ They could face "punishment up to and including death for ANY violating of others rights."
Besides the death aspect to that it's at least consistent with the UDHR, if you were to try and stop some one from having sex with your child you could be put to death despite attempting to act in the best interests of your child.
In the case of some one littering your property if you stated that the punishment for such a crime (it is because You are entitled to property and "No one shall be subjected to arbitrary interference with his privacy, family, home
or correspondence, nor to attacks upon his honour and reputation. Everyone has
the right to the protection of the law against such interference or attacks." to quote the UDHR) is death, you are then braking a human right so if you kill that person so you also get killed (potentially, by some one).
To your point responding to man being greedy and power hungry, it may not be a good argument for government but at least it addresses the idea that people my take more then they need thus creating a large divide similar to what we already have except that these people may have more power to exercise there force the lager they get.
In regards to the economic side of things it's not my strong suite and I know for a fact there is corruption in government that allows for our cash to leek out into the wallets of certain people but is it possible that one of the reasons we pay more now is to accommodate for the upkeep of a lager group of people and other amenity's not all but at least some of the reason.
Homesteading would allow some one to claim extremely large portions of land and not let any one on it; with a large population this would be a problem, creating a larger divide between rich and poor, this usually creates a worse culture and thus worse society.
Also if you accidentally stayed on some ones huge property with out you knowledge you could be punished with death, for arguably disturbing the environment and thus destroying the property.
A few questions can people make there own laws on there property and can they enforce them?
If a privet court lays down a fair ruling then one would assume that they would have to make a ruling in accordance to the laws of the area.
Perhaps you need to elaborate on the laws of this society.