Hanna,
The issue is with the "J!MailAlerts User - Registration" user plugin. I'm not sure what that's doing, or if you need it, but when enabled, it throws that insertion error message. Please let me know if that's critical for your needs and we can investigate further.
I left it *disabled* on your site as that seems to work for now. Please re-enable if you need it for other/normal registrations.
As for PHP 5.3, that version has no issues with JFBConnect, so upgrading shouldn't cause any problems. The older version is not what is causing this problem though.
Thanks,
Alex