Does anything after form_input($in_magazine_page) show up in your post? Since your form opens inside #magazine-form's .panel-body, it's likely that the form will be closed by the browser when you close the .panel-body div.
This may also mean that even if the original file input works, anything added to the .upload-area via JavaScript may be appended to the DOM outside the form. You should be able to see what's going on when you insert the inputs in your browser's debugger.
You could also try changing your script to do this:
Code:
$( "#new" ).click(function() {
$('form input:file').last().after("<div><input type='file' name='image[]' class='input-file'><a class='remove'>Löschen</a></div>");
});
(though you'll have to modify that slightly to keep it from nesting the inserted file inputs inside the wrapping divs)