How can I exclude "Edit My Information" in the edit profile page?

There is a filter hook wpmem_member_links you could hook a filter function to to remove it.

Your theme’s functions.php file is where you would put customizations. See http://codex.wordpress.org/Theme_Development#Functions_File

There is more information on the support site (rocketgeek.com) on how to customize the plugin using filter and action hooks (and other methods).