When pure-ftpd is running the logins can be seen in that log.
Here is what I would do.
Uninstall ISPConfig 3
To uninstall you follow the same steps as you did when you installed except you run:
php -q uninstall.php (in the same directory)
Remove the ispconfig user from the mysql database.
(You can do this in phpmyadmin easily)
Reboot your server
Reinstall ISPConfig 3
If these problems persist then there is something wrong with your setup.