To uninstall Mozilla under Debian, uses Debian's package manager, apt-get. As root, type:
apt-get remove mozilla
Your security program is pretty normal. Microsoft has changed a little bit their system and requires the browser to be with SSL active. Go into www.mozilla.org
and download either Mozilla or Firefox (I recommend firefox, it's very nice and fast, but has less features). The problems you are having with your obsolete Mozilla and hotmail will be gone with a new Mozilla!