This morning, a few minutes after the minyan ended and had begun to disband, a man arrived saying he needed to say kaddish for his father. What we did (with no rav present) isn't particularly important, but now I'm wondering what we should have done. Several questions:
Does halacha permit someone to say kaddish yatom who did not say any of the earlier prayers?
If not and he did it anyway and there's a minyan present, do we respond (amein, y'hei shmei raba, b'rich hu)? May, must, must not?
What about if there is no longer a minyan?
If the answer to the previous questions is "no", are any leniencies available if the mourner is obviously upset? How do we balance compassion and correctness?
While the question arises from a specific incident I hope it's not seen as too localized. I'm interested in the principles behind such a case, not just a yes/no answer.