Well, I don't know how owning air would work. But certainly there could be measures put in place where a certain % of pollution in the environment could be considered damaged property caused by negligence, and thus a community could collectively sue that corporation.
But yes, some scholars have written about it. Rothbard has. Walter Block has a more contemporary view in his book "Economics and the Environment: A Reconcilation." He also talks about these views here and here on YouTube.
And here is a list of other free market environmentalists, mostly economists.
>Also, it everything is owned, would every street be own?
Theoretically, yes. It could be owned and maintained by the community voluntarily, or it could be offered as a service that you pay for annually, or it could be paid for through tolls. It probably wouldn't be the case where every street is owned individually, but a network of roads.
This may sound undesirable, but remember that citizens already pay for these things whether they use them or not. By putting it in the hands of voluntary contracts, better arrangements can be worked out. People that use the roads more would pay more, people that don't use the roads will pay less. Coincidentally, Walter Block also writes about this extensively in his book, "The Privatization of Roads and Highways" (full PDF)
>Would someone who just owned a house be trespassing once he left his property?
It's theoretically possible, and this is one objection many people have, including other libertarians. In such cases (which would be rare, I presume) the community/local courts would have to work something out. Technically speaking, surrounding someone's property where they can't possibly escape (or have to pay a fine) is a form of kidnapping (and in my opinion that would be a violation of the non-aggression principle).
In such a society, I don't think every single thing would be owned. There would, at least, still be walking space and other open, plentiful resources (including some natural resources like oceans, rivers, and forests). However, most things that are scarce and valuable would have the potential to be owned privately. If fishermen value clean and healthy water, they may collectively bind (unionize) and own a part of the ocean to protect against certain corporations that may damage those resources.
Hi there. Welcome to the sub.
I'm not a big fan of what-ifs - I won't bore you with my standard old-man story about the grasshopper and semi-automatic weapons to explain why. But read, watch, and think about it.
For your consideration: http://peacefreedomprosperity.com/7251/dr-david-friedman-how-do-you-stop-air-pollution-in-a-free-society/
Also: http://www.daviddfriedman.com/Laws_Order_draft/laws_order_ch_4.htm
And here ...
Also, Walter Block