Is there a keyboard shortcut for replying to messages, much like the up arrow is a shortcut for editing your previous message?
Not built-in to the chat system, but SEChatModifications adds the capability. You hit Ctrl+Up until you've selected the message you want; in this screenshot I hit it three times:
Then you can hit miscellaneous keys to perform different actions on that message; r replies
For Chrome users who can't install the tool in Michael's answer, there is something in the Chrome Store, but it's not nearly as cool.