I found something that is strange...
The first text field for entering the name has always shown the red background alert correctly. But if I change the label for the first text field to "Full Name:" instead of "Your name:", the red background alert no longer works. And if I change the label back to it's original label "Your name:", the red background DOES work as it did at first.
Still unable to make the email text field red background alert work in firefox and wondering if this cause and reaction (described above concerning changing the label for the name text field) could be a similar issue to what is happening with the email text field not showing it's red background alert, though I have not changed the label for the email field; this label is named as it was originally out-of-the-box.