No. There is no way to send e-mail in the background, client-side. You can, in theory, use the "mailto:" protocol... but that is very messy and doesn't work in every instance (e.g., if the user's client isn't set up properly or they don't have a client to begin with).
Now, as for PHP. Make a file called [font=courier]info.php[/font]. Have this inside of it:
<?php phpinfo(); ?>
Upload this to your server, and then visit [font=courier]yourdomain.com/info.php[/font]. If you see page with a ton of PHP information, you have PHP installed and functioning properly on your server.
If you get this far, all you need to do is then make a file called [font=courier]test.php[/font], and then include the code I previously gave you within it. To "use" the script, just link to the file like this:
You can also type in the ID manually in the location bar, but I'm not sure how you want to approach this.