Not able to access PHP variable

$_POST is an associative array of variables passed to the current script.

So you need to use print_r instead of echo .

window.alert("Variable" + <?php  print_r($_POST); ?> );

$_POST is an array so you should use print_r() or var_dump() instead of echo:

window.alert("Variable" + <?php  print_r($_POST); ?> );

If debugging the $_POST variable in Javascript is what you want to do I suggest you do this:

console.log(<?php echo json_encode($_POST); ?>);

And you'll see the content in your developer tools on your browser.

For reference you can look at the answers to this question.

EDIT:

<form method="POST">
  <input type="text" name="first"/>
  <input type="text" name="second" />
  <input type="submit" value="submit">
</form>

<?php if (isset($_POST)): ?>
  <script type="application/javascript">
    console.debug(<?php echo json_encode($_POST); ?>);
  </script>
<?php endif; ?>

EDIT 2: (after you updated your code)

Change the type option in the ajax jQuery function to method like so:

<script type="text/javascript">
function callAjaxAddition() {
    arguments0 = {
        arg1: $("#exampleForm input[id='pac-input']").val(),
        arg2: $("#exampleForm input[id='pac-input']").val()
    };
    $.ajax({
        method: "POST",
        url: "processAjax.php",
        data: {
            arguments: arguments0
        },
        success: function(data) {
            $("#answer").html('<ul><li>' + data + '</li></ul>');
            send_apptn_req();
        }
    });
    return false;
}
</script>

Also note that after the AJAX POST, your $_POST variable will contain the data object that you passed to the $.ajax function and therefore what you are passing:

 data: {
   arguments: {
    arg1: $("#exampleForm input[id='pac-input']").val(),
    arg2: ("#exampleForm input[id='pac-input']").val()
   }
 }

will translate into:

Array (
  'arguments' => Array (
    'arg1': 'value of arg1'
    'arg2': 'value of arg2'
  )
)

So the loop in processAjax.php is quite useless since you're not looping through the inside array.