If you use wp_get_linksbyname() instead of get_linksbyname() then the list of links will be displayed according to the parameters you set in the 'manage link categories' page. Ditto for wp_get_links instead of get_links.
in order to get updated to work, you need to do a couple of things:
1. Set the option to show updated on the manage link categories page.
2. Under Options -> Link Manager Settings you can specifiy various related parameters for the display of updates. For now I would leave the defaults.
3. Uncomment the line from the default index.php
make sure the file weblogs.com.changes.cache is writable by your web server.
4. And then it should start working.
It will grab the list of updated weblogs (set in options) from weblogs.com once per hour (default, change it in options) and set the updated timestamp in any links you have which appear in the file from weblogs.com.
That last updated timestamp will be displayed as a title attribute (tooltip) of the link. If the last updated timestamp is within the two hours (again, set in options) of the current time then it will use the prepend and append text specified in, you guessed it, options around the link.
Hope that helps,