Debian disable the internal mail completely

You want start_dirty_degraded. Try specifying md-mod.start_dirty_degraded=1 as a boot argument to the kernel image.

If you want a quick to setup solution for monitoring mysqld processes, disk usage, Apache2 and resource usage I would suggest to use monit with an external google smtp service configured in /etc/monit.conf like so;

set daemon  60
set mailserver smtp.googlemail.com port 587
    username "Rabbi" password "Loew"

set alert myadminuser@gmail.com but not on { instance } with reminder on 15 cycles 

#grab some service scripts
include /etc/monit.d/*

set httpd port 2812
        allow 127.0.0.1

I have the following in /etc/monit.d/filesystem.conf

check device rootfs with path /
    if changed fsflags then alert
    if space usage > 90% for 5 times within 15 cycles
      then alert else if passed for 10 cycles then alert
    if space usage > 95% then alert
    if inode usage > 90 % then alert

and something like this to alert of resource usages as appropriate in /etc/monit.d/system.conf;

check system localhost
    if loadavg (1min) > 10 for 10 cycles  then alert
    if loadavg (5min) > 60  for 10 cycles then alert
    if memory usage > 90% for 8 cycles   then alert
    if swap usage > 20% then alert
    if cpu usage (user) > 90% then alert
    if cpu usage (system) > 75% then alert
    if cpu usage (wait) > 75% then alert

I've also started a github project called monit-shared which aims to capture a few starter configurations for common services (sendmail, dovecot, mysql) etc.

You can generally just checkout which ones are applicable into /etc/monit.d, such as httpd.conf and they should do the kind of basic checks you mention automatically, and notify using your external email service.