@ Ze’ev Ionis
The pagination and character index use the same code regardless of the template in use. You mention “home page”. Are you talking about the page set as the WordPress static Home Page? If so, is that also the page you have set to the Directory Home Page? If so, the issue is with WordPress. Permalinks for plugins will not work correctly because WordPress “routes” the query as a “blog” query so nothing will be found when clicking the links for Connections because they are not a “blog” post. The solution is not to put the directory on the site’s home page.
Hope that helps. Please let me know.