I agree with 2 and 4. Rights are crucial, but they should be exercised in a responsible manner. Of course, definitions of "responsible" conduct are open to dispute. The old argument that the right to free speech does not allow a person to shout "fire" in a crowded theater is one with which most people would agree, but there are many situations that would cause far more controversy, such as the current Occupy Wall Street protests.
As #2 says, the two are often intertwined. My right to free speech, for example, entails a certain responsibility not use that speech to slander others. Because we live in society, no rights are absolute, they are relative to the rights of others. So while you do not have to ask permission to exercise a right, you do have a responsibility to exercise it within certain boundaries. There are other types of responsibilities, of course- those that aren't necessarily created in this societal context, but those are largely moral, the kinds of responsibilities we wish people would uphold- concern for the less fortunate, for instance.
That's a bit of a catch 22. People have to be responsible in order to take advantage of certain rights. Yes, we believe that all people have certain rights, but we have to responsible for those rights in order for them to be achieved. In the US for example, people have the right to bear arms, but with this right comes huge responsibility. People have to be responsible in the way they exercise this right or they do not deserve to have it. On a more fundamental level, any person should have the right to live in humane conditions. People all over the world are responsible for making this right come to fruition. We must all take care of ourselves as well as our neighbors and do what we can to promote humane treatment of others. Yes, the right is fundamental but the responsibility is what drives the achievement of such rights.
In some societies they are, but they should not be.
Legally, rights should be more important. Rights should be legally protected while most responsibilities should not be. Morally speaking, however, we should be as keen on fulfilling our responsibilities as we are on protection our rights. We should realize that we need to act in ways that help to keep our society strong rather than simply doing whatever we want because we have the right to do so.