I'm quite confused about Sartre and his relationship to morality. He talks a lot about responsibility. When I think of responsibility, punishment and law come to my mind. But I suppose Sartre's responsibility means that we have to accept that we have by our free decisions contributed to how things have evolved. Do I understand it correctly? But can we derive from this existentialist responsibility a reason why we should not, for example, kill someone? Is the fear of being put in jail the only thing that will prevent us from doing so?
Existentialism (along with absurdism, phenomenology, and a few other schools) is a descendent of Nietzsche's worldview. It carries over Nietzsche's lionization of the individual, and his radical distrust of socially derived value structures. To that end, Sartre, like Nietzsche, locates morality as a feature of the 'authentic' self. For Sartre in particular, we can only achieve a proper moral understanding when we have disabused ourselves of all of the social, cultural, and political understandings that we have been indoctrinated or subjugated into (including, interestingly, the concept that there is a transcendental ego underpinning the self).
This is where the notion of 'responsibility' comes into play. We have a natural tendency to flee our authentic self in favor of the socially-determined self presented to us by our environment. We must (for Sartre) take the responsibility of sticking to the existential paradigm and freeing ourselves from this false ego, and as we discard these external moral structure, we create an authentic moral context.
Sartre does not explicitly get into moral questions like whether we can kill others, except to suggest that the basic structure of authentic morality is the pursuit of freedom, and so we cannot 'authentically' restrict the freedom of another (through enslavement or murder). If I were to extend Sartre somewhat, I might suggest that the moral quandary of whether to kill another only arises for the false, socially-derived ego. In other words, our social environment conditions us to be a certain kind of person, act in certain ways, desire certain things and despise other things; part of that conditioning is a reflexive violence against difference, non-conformity, and actual authenticity. When we dispose of the conditioning, we dispose of the reflexive violence as well, so we would never feel an authentic urge to kill or harm another. But again, I'm reading that into Sartre (and probably importing a little Buddhist philosophy to boot), so don't take that as a verified existentialist position.
"But I suppose Sartre's responsibility means that we have to accept that we have by our free decisions contributed to how things have evolved. Do I understand it correctly? "
Yes. This is only one implication of the main idea which is:
We are only responsible ( = have to give a response ) to ourselves. Other implications are:
If you agree with yourself then others' judgement are irrelevant. If there is someone you can blame, then it is you. If there is someone you can be proud of, then it is you.
For example, if someone wants to kill you because it makes them happy, do not waste your time blaming them as they are only responsible to themselves, not to you. You can blame yourself for not having done the necessary to protect yourself, or be proud of yourself because you have actually done the necessary...and so on and so forth..
As you can see, this is clearly not what a priest will tell you about morality !!
I hope this helps.