unset the timezone and group in the profile form
The reason is because your module in which you write you hook_form_alter has a weight of 0. In your database table "system" for your site look for your new module's row and edit its weight to a higher value. I set mine to 100. After you do this "clear your caches" just in case. Then you should now see the line item in your $form variable this is "timezone". Now your unset should work.

unset($form['timezone']);

Keep in mind that if you uninstall your module you will have to re set the weight again. 

If you add this in your "MYMODULENAME.install" file you will be able to set this on intall

    /**
     * Implementation of hook_install()
     */
    function MYMODULENAME_install() {
      // New module weights in core: put MYMODULENAME as the very last in the chain.
      db_query("UPDATE {system} SET weight = 100 WHERE name = 'MYMODULENAME'");
    }


Hope this helps