Good points there.
1) If the original owner is unknown or there is no prior owner then it is up to majority acceptance which defaults to "who ever uses it first".
Majority acceptance is only possible by majority vote which is a (democratic) state of some sort.
"Uses" is very vague and assumes people would only claim what they need for now: Say I and 100 other migrants come to the US of the 18h century. I (and possible all the others) then claim to "use" some land. Assuming that it is my goal to extract the most profit out of this land rush opportunity I will try to "control" as much land as I can. So my argument is that land is claimed and defended by private force until the majority (some form of state) accepts that it is yours.
3) Environmental problems are handled the same way as vandalism. Property owners file a public complaint and if found to be valid (details left out here) results in the vast majority of individuals and businesses actively shunning and denying access/service to the individual who is guilty of vandalism until they make restitution.
That would require every land and every resource to be private property. Rivers for example, coming back here to point (1), have historically never been "first used" only by one person or one company so there is no ethical and no practical ground for establishing private ownership of it other than when a state is selling it. But that is possible and practicable. A problem here could be the short term profit orientation: Shareholders of the river property might allow a certain (possibly too high) introduction of chemicals by local factories into the river (against a fee for doing so) which would not be a problem in the short term (which is the time frame for profit extraction) but would be a problem in the long term.
Environmental issues often are related to common pool resources: What if the resource can not be made private: For example the quality of air in a city. Everyone is using/enjoying/living by a not too polluted air (pollution through cars, factories etc.). The only way to keep the air quality good (enough) is to find a majority consensus about an acceptable degree of air pollution and then agree on measures to enforce it. Those measures have to be enforced also onto those that do not agree with the majority consensus. That is a state like structure: The state has the monopoly of force to enforce decisions (to not pollute the air) made by indirect majority vote (democratic state with delegation of decision making).
The air pollution example is far fetched in not densely populated areas (most of the US) but an issue in most parts of the world, especially in China - it should just serve as an example for commonly used goods which can not be made private.
Another example is: A good can be made a private good in so far as it is possible to restrict its use (precondition for making it a private good which was not possible in the air example above) but it can not be made a private good in so far as its effects are global: Parts of the rainforest in South America are made private or at least there is no efficient state to prohibit the "initial use" of this land. People (local farmers as well as global companies) tend to do with the land what is most profitable for them which mostly is to burn it and grow foods on it or cut the woods and then grow food on it. In each case a common good is harmed motivated by the (natural) profit / survival interests in the forest. The common good is that the rain forest plays an essential role in global climate stability which is a resource (the stability/continuity of the climate not how warm/cold it is) everyone on this planet profits from and it is a common resource since it prevents floods everyone bad by harmed by that lives in the area (but does not profit from the rain forest like the farmers/companies do).
Now a Brazilian state doesn't help much here. Since it is a resource every human being is depended on and uses continuously there would need to be a global solution. For example: Giving every human being the same amount of not locally restricted resources (the same amount of greenhouse gases that each individual can consume; the same amount of pollutants to various ecosystems that are all common goods and can not be made private goods by definition) and put that on a blockchain and require individuals and companies to trade it. Downside: It would require measuring everyone's pollutants output... :/