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I can see the colored dots indicating current commenting status, but why aren't they clickable?

The commenting status link/button is only clickable is you have JavaScript enabled.

What does the color-coding of the dot mean?

Green means the post is currently open for comments; red means the post is not currently open for comments.

How can I customize the color-coding used for the dot?

You can customize the colors via CSS. .comment-state-1 indicates comments are open. .comment-state-0 indicates comments are closed.

How can I customize the dot used to represent commenting status?

By default, commenting status is represented using the • character. You can change this by filtering c2c_one_click_close_comments_click_char. Here's an example -- added to a theme's functions.php file -- to change it to a solid diamond:

add_filter( 'c2c_one_click_close_comments_click_char', create_function('$a', 'return "&diams";') );