There are a few issues here. The first is the one that is actually posed in the question. The solution to this is changing
header('Location: http:/www.example.com/success.html'); to
header('Location: http://www.example.com/success.html'); (I know that you actually had
mysite.com, but we're not allowed to use that in answers.
The second issue is that the form is posting to an HTML page, when it should (almost certainly) be posting to a PHP page.
<form method='post' action='success.html'>. Since you said that all of the code you provided was in index.php, I suggested
<form method='post' action='index.php'>
That said, having all this code together in one file is quite hard to follow and tends to lead to confusion and errors. Following the principle of separation of concerns, you should split your form-handling code out into a new file that simply decides what to do with the submitted data and acts appropriately. Any HTML should be in its own file as much as possible.
If I had to guess, I'd say that this never actually worked 100% in your testing environment. Instead, the errors were probably just masked.