Can we cultivate ethics or morals from Sartre's existentialist perspective? What does he mean by a world where not only God does not exist but “Man” too? Is it a different world than Nietzsche's description of our epoch where “God is dead”? Can we say that existentialism is a new religion?
I think there are real problems with the idea of developing and ethics out of existentialist philosophy. I know Kierkegaard better than Sartre, so I'll say what I think is wrong with his view.
Kierkegaard thinks that Hume has shown, pace the history of philosophy before him, that morality (understood as a body of universally binding commands that hold for all people at all times and places) cannot be derived from reason.
Kierkegaard also thinks that Kant has shown, pace Hume, that morality cannot be derived from the passions either, for the passions are individual, contingent and historically variable.
Kierkegaard thinks that the source for the binding authority of the moral law, therefore, must come neither from reason, nor the passions, but rather the very phenomenon of choosing itself. His idea is something like: If you really have to face up to the terrifying fact that there aren't external, objectively given sources of moral authority and that you just have to take the leap of faith and make a moral choice, then you are going to choose the right thing. Kierkegaard's idea is that the idea of the leap creates anxiety, but that everyone who faces that anxiety authentically will choose to live a moral life. He doesn't mean that whatever they choose WILL be moral--he isn't a subjectivist about morality. He thinks that if you seriously consider, for instance, whether to live a life of sexual debauchery, or marital fidelity then you will realize that marriage and a family is the only choice worth making.
Kierkegaard is obviously wrong about this. Just realizing that you have to make a choice in no way indicates that you are going to make the right one. I don't see the existentialist point of view here being any superior to Hume's famous dodge that even though there isn't a rational foundation for morality, that doesn't lead to skepticism, because morality is based in the passions and everyone has the same passions. It seems to me that it is shared cultural and historical baggage in the background that is doing all the pushing in the moral theories of the enlightenment.
If you'd like to hear more about this, I'd recommend chapters 4, 5 and 6 of Alasdair MacIntyre's After Virtue.