How can I move just one email within a conversation (a response from one person within a conversation for example) into a label/folder without moving the entire conversation?
You can't, really. When you're looking at the conversation it shows all the labels on all the messages.
The only way to really do that is to turn off conversation mode, but that's like using TNT to kill a fly.
One hack-y thing you could do is forward the message to yourself (and be sure to change the subject line). Then label that forwarded message as you like.