You are asking for $_POST['submit']
which is never set, because no input field or button of your form is named "submit".
Change your button to:
<input type="submit" class="btn-default" name="submit" value="Send it">
or set a hidden field named submit:
<input type="hidden" name="submit" value="value">
And then your redirect will fail with the "Header already sent" error, because you must not have output before a header()
call.
Put the header()
call in an else
part of your if($_POST['submit'])
The same is for every other input field. The name is missing. Instead you use the name as the type. The type should be "text" everywhere.