I have tried to set-up an email.html and an action.php so that someone can send an email from a website. Here is the code in email.html
First check result of the mail. You also should check the php error log file.
when your mail is really going out, use an valid sender email, the you can get bounces from the receiving mail server.
don't forget, there are many anti spam technology's. most important is that you respect and know how SPF is working. that's one of the most fails, websites doesn't send emails which don't arrive at recipient.