Hi

Replace <ul><li> in link.html template with:

<%if category_id%>
<%elseif link_results%>
<%else%>
<ul><li>
<%endif%>

Replace </li></ul> in link.html template with:

<%if category_id%>
<%elseif link_results%>
<%else%>
</li></ul>
<%endif%>
to replace </li> </ul>at the end of the template also.

This should stop the <li><ul> showing in the search and categories.

If you want to email your link template I'll make the changes and email back.
PM me for the email address.

In regard to making a new template, there's really nothing to it, just need to save
link.html to new_link.html and upload that to your server default/local directory.
Or if you do it in Admin just open up the template and save as the new name by changing the "Save template as" option at the bottom.

Regards

minesite