Capitalism is simply the codification of a monetary transaction to which both parties agree. As long as there is supply and demand (finite resources) there is capitalism.
We have democratic socialism to make capitalism less brutal (read: less efficient but more humanizing) but demand is too fickle for most economies to be centralized much beyond that.
Not really. A lot of today's capitalism is based on concepts such as copyright, patents and trade secrets, which are definitely not "natural" - in fact, they are directly opposite of "free market".
Personally, I believe that a capitalistic system where these three are eliminated or at least severely restricted would be much preferable to what we have today.
Could you please elaborate on how the world would look like without these three concepts?
Ownership is a form of monopoly as well.
Just because a resource is rivalrous doesn't mean more than one person couldn't be permitted to use it, particularly when you're talking about capital goods.
They are not "the" rights of ownership, they are a particular set of rights of ownership.
Once upon a time people were included in the set of things people had a right to own, and ideas weren't. These things can change. The rights we have now are just those we currently think of as most correct.
No, that's just a market. A necessary, but by no means sufficient condition to label an economy capitalist. That's why the new word "capitalism" has been introduced to describe the difference.
You could imagine (as a quick, not particularly explored example) a society where there's only a market for labour, and the state leases all durable goods, and sells or provides all consumables.
Yes, absolutely. For a system to be capitalistic, you also have to have at least capital intensive means of production (hence the name), a real labor market and more or less free access to the market both as a consumer and a producer. Capitalism only started existing with the onset of the industrial revolution.
Reductio at absurdum: A Greek citizen in 200 BC is buying fish from a fisherman, with coins, at freely decided prices. Thats the market at work, but no capitalism at all.
That depends on your definition of "capitalism" and "economy".
If you use "capitalism" in contrast to Mercantilism and feudalism – which seems to be a rather unpopular view in English-speaking countries for some reason –, then it makes perfectly sense.
Although it would help to actually read it.