1. How is property the product of my life and liberty? It is only to the extent that I valued it during my life, period.
2. You don't get to define the purpose of government and it isn't limited to your worldview.
3. Why bother if there needs to be catch all?
4. Who gets to decide which ideals are best pursued by government vs individual? Then you get into silliness on the order of gibbsian delusion.
1. I don't even know what you are saying. Property is the result of your life and liberty: If you work to buy a Corvette, it means you are spending part of your life and liberty to earn that Corvette. If someone steals your Corvette, they stole something that you actually valued more than your life and liberty that went into earning it.
2. But it's limited to yours? You didn't even account for non-democratic governments and you are talking about my limited world view? The whole point of libertarianism is that nobody knows what's best so you can't centrally plan society. It doesn't matter what my world view is, because under my ideal government, I'm not allowed to push it on you.
4. I'm an anarchist*, so nobody should get to decide, IMO. Since a libertarian society is the next best thing, I'll settle for that. A libertarian society is very simple. As long as you cause no direct harm to others, government will leave you alone. In
The Law, Bastiat argues that government shouldn't be able to do anything the people cannot do themselves, otherwise you inevitably will have despotism.
* You seem to have trouble wrapping your mind around libertarian principles so it probably wouldn't be useful to probe me about how an anarchist society would function. If you are interested,
Machinery of Freedom lays a decent groundwork.