Hi Radiok, thanks for your reply. It was a weird thing - readers registered, I verified them manually, but then their user name just disappeared.
I've since disabled the RPRedux "e-mail verification" and "admin verification" options. Also the password strength meter. I eventually deleted all members and asked them to re-register after changing above settings. I added no additional fields.
Working well now, but of course not the way I want it.
The only settings I have are "Customer New User Message" and "Custom Admin Notification". And I've added a logo. That's it.
Other plugins:
Aksimet; Breadcrumbs Plus; Configure SMTP; E-mail Users; List Category Posts; Members Only; Reg Plus Redux; User Login Wiget; WP Stats; WP Downloads Manager
Theme - Woo Themes Typebased
Hope this helps. Thanks again for your work.