That's the sort of Hobbesian definition of freedom, sure. It's the ability "to buy, and sell, and otherwise contract with one another; to choose their own aboad, their own diet, their own trade of life, and institute their children as they themselves think fit; the like." Freedom in this sense is allowing decent people to do reasonable things.
There's also another view of freedom, found in Christian philosophy. It's the freedom of self-mastery. It's the kind of freedom Saint Augustine was talking about when he claimed that the "virtuous man, though a slave, is free." It's freedom from passion, freedom from irrationality. It's the freedom to pursue what on ought to do as informed by one's own reasoning faculties.
Certainly, there's nothing mutually contradictory about these two kinds of freedoms in my book. In fact, I'd say they are both necessary for a good society. But the former kind of freedom is an effect of good governance; it's what happens when people are safe and there's a well-established order to things. It only exists in a world where the state doesn't feel the need to micromanage people's lives because the people aren't going around destroying themselves and each other. In other words, the former kind of freedom can only exist in societies where the latter kind of freedom is shared amongst the citizenry.
I don't quite understand what you mean. A right is, from what I see, an object of justice. It's something owed to an individual or a corporate body as a matter of justice. At its most basic, I believe that all rights amount to the right to do what one ought to do because, as Kant pointed out, ought implies can. Rights, therefore, have a teleology to them in that they exist for a purpose - to help us pursue virtue. We can therefore never have a right to do wrong.
Million dollar question there. Complicating things are the ideas of political rights (rights you have as citizens) versus human rights (rights you have as human beings). Voting is a citizens' right, not a human right, for instance.
Actually, "yelling in a crowded theater" is an outdated standard. I would read
this article a bit to understand what I mean.