The problem on the admin side is an apache mod_security fault that confuses a cookie with a sql injection. See here: http://www.satollo.net/apache-mod_security-and-newsletter-and-block-access-error.
About the cron: Newsletter register it’s own cron type that should fire every 5 minutes. If that cron is, for any reason, disabled by other plugin it may not work. It happened in the past with some plugin.
Can you send me the list of plugin you’re using?
Try to install the plugin wp control plugin which lists the scheduled task and the available shedulers.
http://wordpress.org/extend/plugins/wp-crontrol/
Stefano.