@ Jonathan
Ok, I think I understand, maybe. The references to the /user-edit.php?user_id={$u}
code you been making is the WordPress admin Edit User profile page which does not have anything to do with Connections.
Unfortunately it is impossible for me to answer your question because I do not know the code you have used to build your search. For example, what function is being used to to set the $results
variable. If it is not the core Connections function for retrieving entries based on search params there is no way to get a link to the Connections entry because the entry ID would be needed.
If you need a directory search then I highly recommend any of the premium templates which include this feature or the Widget Pack which includes a search widget that can be used to search the directory.