So, first off, let me say that if it'll help us move toward something better than we have now, even if in my head I call it anarcho-communism, I'll happily call it "capitalism."
For reference, there's an author named Charles Eisenstein who in his book "Sacred Economics" advocates for taking steps that he intends to move us (the world, I guess) eventually to a gift-based economy without money or barter. And he calls it capitalism. With a straight face. Now, I don't know if deep down in his heart he believes it actually qualifies as capitalism or if he's calling it capitalism because he feels like his aims are more likely to be well received by pro-capitalists if he calls it "capitalism."
One can IMO go too far with that. Case in point: ecofascism. But I digress.
On to the definition of capitalism. At least in my head, capitalism is characterized by:
The profit motive. The incentive to amass. (Typically money, but a barter-based system could well be the same in every way that matters.)
Quid pro quo. The whole system is based on it.
Private property. A particular set of rules for who has ownership rights over what.
The institution of employment.
My answer didn't include the word "capital", so I'll skip that second question.
As to your third question, let me take exception with the question itself. I don't believe "control over what you produce" is necesssarily a good thing per se. I believe in having something roughly like ownership rights over what one uses. But if one produce a surplus, I don't believe they should be able to deprive others in need of said surplus.
I think capitalism coerces people into producing surplus for others to sell for a profit that the producer (employee) doesn't get a fair share in if that goes more to the spirit of your question.
Bonus questions:
I... don't know or care? "Capitalist" can mean someone who supports the institution of capitalism. Or it can mean something like an owner of a company that employs people. I think plenty of people participate in capitalism (by selling things they make, by accepting an employment position, etc) out of necessity while disapproving of the system as a whole. Hell, I'm one of them. I'm not sure I understand why you ask.
If I'm the person who sells things I make? Again, anticapitalists participate in capitalism because capitalism doesn't give them a choice. Does that answer your question?
The word "sell" here has some baggage I don't like. I'm not for a system in which anybody "sells" anything. But to answer how one might expand an operation that produces things, worker cooperatives are probably the most obvious answer.
Anyway, worker cooperatives are owned and run by the workers. Corporations are owned by shareholders and run by boards of directors. Worker cooperatives don't have incentives and power to fuck their workers over. They do have incentive and power to take care of their workers.
Maybe I should have read the first thread you referenced before answering these. Maybe it would have given more context. But hopefully this response gives you what you were looking for.