what exactly is your question? is it: how come mozilla doesn't start when i click on it's icon?
Are you sure the path to mozilla for the icon is /usr/local/mozilla/mozilla/mozilla? That would be totally wrong. As you can see from the results of your whereis query, mozilla is at /usr/bin/mozilla. You should be able to look at the properties menu of your icon and under the 'execution' tab, just put in "/usr/bin/mozilla". The icon is really only a link to an app or file that has already been set (by you or your install).
If I didn't get your question right, just re-ask it in a question form.