Is the script you posted in your first post the entire script? (if not, can you post the whole thing?)
If it is, does the "successfully submitted" message appear? If it does you're getting through the script ok. But once you've printed that message to the screen a redirect will have to be done with a link the visitor has to click.
The better way would be to comment out that last print command and add:
header("location:".$redirectURL);
That should make the redirect happen for you. Note that nothing else can print/echo to the browser before this line or the redirect will not happen and you'll get an error about not being able to add headers because output started on line X.
On the email problem (I'm assuming you're hosting with a hosting company and this is not your own server) try creating a seperate script just to test email functionality. If the server isn't correctly configured email my simply not be available in a functional way.
If that is the case try using a mailer class that attaches to another mail server (SMTP) to send the message. Your host provider should be able to provide you with a server that will accept the connections. The mailer class that I prefer is http://phpmailer.sourceforge.net/ Of course, your mileage may vary (YMMV) and there are a number of these classes floating around with more or less the same functionality.