Even if he manages to find it, would it still be considered his property? 
As far as I know, in most countries, whatever lands in the trash becomes property of the city/government. So even if he finds it, the government could easily sue him and take it back? That would suck but for almost a billion USD, I imagine that would happen.
And what happens if someone else finds it first? Is it still considered his property, legally? He threw it away so he relinquished the ownership rights?
He only threw away the privat key, not the bitcoins. They are still safe where he last moved them in the Blockchain. So if someone else finds the privat key and moves the 8000 bitcoins to another address in the Blockchain. He will claim someone stole them.As far as I know, in most countries, whatever lands in the trash becomes property of the city/government. So even if he finds it, the government could easily sue him and take it back? That would suck but for almost a billion USD, I imagine that would happen.
And what happens if someone else finds it first? Is it still considered his property, legally? He threw it away so he relinquished the ownership rights?