Again: what would stop a big corporation or a big group of people to just take a big chunk of space and then another and another and another. Small groups would never be able to establish themselves.

Take how? In an AnCap society people have guns to defend themselves, if you mean taking by power. People can organize themselves to get shared-spaces. AnCap society does not necessarily means everything is private.

Besides that, if you don't like how the society works, you're free to abandon it and live a nomad life, consuming what the nature gives you. Nature isn't suddenly going to disappear just because AnCap. You'll have to hunt, or fish (No one can claim property on the sea or all coast line). If this kind of work for your survival oppresses you, then I dunno.

Like /u/the9trances said: "And if one property owner says, "no, you can't fish here," there are a dozen others. And there's also a good chance wilderness isn't private property, because you must establish ownership in the community of an area for it to be considered "private." So there will be a lot of wilderness, unsettled land, that's eligible for foraging or homesteading. Homesteading is the process where wilderness is turned into private property through usage of an individual or a group."

Actually not. Nestlé is already doing this.[1] And I highly reccomend this doccumentary.[2]

I'll see it when I can. I don't know what the documentary says, but be aware that the water in those places are polluted, and Nestle actually treat them, mineralize it, and then sell clean drinkable water. The highly polluted waters and dysfunctional water treatment in these countries are not Nestle's problem.

That's true, but there's lots of studies about how deforestation is growing on developing countries. Polution levels keep growing on big cities...

Still, cars today are a lot more efficient and cleaner than 10 years ago. Hybrid cars are getting more accessible. Solar Panels are getting greatly effective and cheaper.
It's not a big stretch to say that soon the pollution growth will slow, or even diminish. Ecological and environmental thoughts are relatively new in our society. People are getting more conscious about how they can affect the world, and this demand reflects on the market.

while it's true that capitalism does not a full destruction of resources but you can't deny that it destroy the planet.

It does not destroy the planet. The planet has been through worse. But it can destroy ourselves.