I’m not sure about your problems with the Links Manager – I just let my blogroll languish behind my reading list in Bloglines. But for your formatting problems, have you read the Codex documentation for get_links? You should be able to do what you describe.
Does it give you stats specifically for the “entry” pages of a session? Any sessions that begin by hitting wp-rss2.php are almost certainly RSS readers.
There are also plugins that can track that sort of thing; I’m using BAStats.
The other possibility is to route your feeds through an external service like Feedburner.
Have you tried <?php echo wp_specialchars($s); ?>?
