About the "read more" link
No, and yes - sort of, in order.

The teaser system assumes that there will always be more to read so if you choose to show the teaser, by default it will always have a 'read more' link.

You can, however turn off the link entirely quite easily.  Copy node.tpl.php from your main theme into your custom theme directory and comment out this part:

&lt;?php print render($content['links']); ?&gt;


If you only want to show a read-more link when there is more to read, you almost certainly need to build a custom module for that.  There's lots of good documentation on how to do that, but we can probably help with the specifics here once you have a framework going if that's what you decide to do.

Note that if you only want to change the behaviour for a particular content type, put some logic around the line instead of commenting it out, like this:

&lt;?php if ($node-&gt;type != 'article'): ?&gt;
  &lt;?php print render($content['links']); ?&gt;
&lt;?php endif; ?&gt;