PHP: Possible to automatically get all POSTed data?

Sure. Just walk through the $_POST array:

foreach ($_POST as $key => $value) {
    echo "Field ".htmlspecialchars($key)." is ".htmlspecialchars($value)."<br>";
}

No one mentioned Raw Post Data, but it's good to know, if posted data has no key, but only value, use Raw Post Data:

$postdata = file_get_contents("php://input");

PHP Man:

php://input is a read-only stream that allows you to read raw data from the request body. In the case of POST requests, it is preferable to use php://input instead of $HTTP_RAW_POST_DATA as it does not depend on special php.ini directives. Moreover, for those cases where $HTTP_RAW_POST_DATA is not populated by default, it is a potentially less memory intensive alternative to activating always_populate_raw_post_data. php://input is not available with enctype="multipart/form-data".

Yes you can use simply

     $input_data = $_POST;

or extract() may be useful for you.

All posted data will be in the $_POST superglobal.

http://php.net/manual/reserved.variables.post.php