Welche [Liste] and
welcher [Mann] are correct. It's either
welche (die) or
(Edit: I misunderstood your question about the ending. But now that I wrote the whole text about adding the word, I'll just keep it.)
Now to the difficult question whether you add [something]. I would say you add the word when you're not sure that there is a something. Some examples:
You have a green, a blue and a yellow list. If you say
Ich mag die Liste nicht.
and the other person knows that there are these three lists, he/she would only ask
Welche? because it's clear you're talking about those three lists.
If you do not have any list -- or if the other person doesn't know of any list -- she would ask
Welche Liste? emphasizing that she's slightly surprised you're talking about a list.
To your second example: If we're in a zoo and there are plenty of people around us and then you say
Der Mann ist affig.
I would probably ask
Wer? because it's clear you're talking about a man and a person next to us.
If you would ask while we were walking through the streets (and there where a couple of men but it was not so clear which one you were talking about) I would ask
And if we were alone and there was no man around us (and you were talking about a man you've seen before) I would ask
Welcher Mann? because I have no idea which man you could be talking about.