Are you trying to run a program that needs X from a non GUI environment (runlevel 3, no X running)?? If that is true: You cannot do that. X must be running.
About your 'schedule problem':
You need crontab for the sheduling:
00 11 * * * /full/path/to/program
I don't know the mozilla syntax, but if it's like opera's it looks like this:
Put both together:
00 11 * * * /full/path/to/mozilla www.somewhere.com/my_web_mail.html
You might need to take care of any error messages that might be send to stderr, if that is the case, change the above example to:
00 11 * * * /full/path/to/mozilla www.somewhere.com/my_web_mail.html 2>/dev/null
Like I said in the first part: X (and a windowmanager) must be running, 'cause mozilla needs it.