How to view data from DB with AJAX immediately after script counts it?

I am practising AJAX by implementing editable HTML table looking like this:

The logic is this:

1. User clicks on left column (containing integer);

2. JS script catches its value and by using AJAX adds them to database;

3. PHP script fetches this value, makes some calculations, adds them to database and shows result in right column (date in <td>).

Now as expected PHP script needs page refreshing to show calculation result (date in <td>). I'm trying to write JS script which will retrieve calculated data from database and immediately show in HTML table's cell. Having troubles with it. Asking for help with this issue.

index.php:

<form id="form-wrap" action="functions.php" method="POST"> 
<select name="select1" required>
  <?php 
  for ($i = 1; $i <= 20; $i++) {
  echo "<option>".$i."</option>"; 
  }
  ?>
</select>
 <br>
 <input type="text" id="name" name="name">
 <input type="date" id="day" name="day">
 <input type="submit" name="button_ok" id="button_ok" value="Write">
 <input type="submit" name="show" id="show" value="Show table">
</form>

functions.php:

<?php
require_once 'dbconnect.php';

$loged = $_POST["name"];
$day = $_POST["day"];

class Count_Add_Class { 

  public function CountDays() {

   global $day, $loged, $day_remind1, $days_before1;

   $currenttime = time();

   $days_before1 = $_POST["select1"];

   // ... make some calculations with user's input ...

   $this->AddDate();

   }

  public function AddDate() {

   global $pdo, $loged, $day, $day_remind1, $days_before1;

    if (isset($_POST['button_ok'])) {

     // ... insert in database user's inpt and calculation result ...
   }
 }

}

$obj = new Count_Add_Class();
$obj -> CountDays();


function Count_days_new_data() {

  global $pdo, $day, $loged, $day_remind1_updated, 

  $stmt = $pdo->prepare("SELECT select1 FROM tablex WHERE name=?");

  $stmt->execute([$loged]);

  $res = $stmt->fetchAll();

     foreach ($res as $row) { 
          $day_remind1_updated = $row['select1'];
     }

   $day_remind1_updated = $day - ($days_before1_updated * 86400); 

   $day_remind1_updated = date('Y-m-d', $day_remind1_updated);     

}

Count_days_new_data();


function Show() {

 global $pdo, $loged, $faq, $day_remind1_updated;

      $stmt = $pdo->prepare("SELECT * FROM tablex WHERE name=?");
      $stmt->execute([$loged]);
      $faq = $stmt->fetchAll();

      $s1 = $_POST['editval'];
      $id = $_POST['id'];

      $stmt2 = $pdo->prepare("UPDATE tablex SET select1=? WHERE 
      id=?");
      $stmt2->execute([$s1, $id]);

      $stmt3 = $pdo -> prepare("UPDATE tablex SET day_remind1=?,WHERE 
      id=?");
      $stmt3->execute([$day_remind1_updated, $id]);

      require_once 'table.php';   

} 

Show();

?>

table.php:

<div id="day-data">
<tbody>
<?php
    foreach($faq as $key=>$value) {
?>

    <tr class="table_row">
    <td><?php echo $value['name']; ?></td>
    <td aria-label="First" contenteditable="true" onBlur="saveToDatabase(this,'select1','<?php echo $faq[$key]["id"];
?>')" onClick="showEdit(this);"><?php echo $faq[$key]["select1"]; ?> 
    </td>
    <td><?php echo $value['day_remind1']; ?></td>
    </tr>

<?php
   }
?>

edit.js:

function showEdit(editableObj) {
   $(editableObj).css("background","#FFF");
 } 

function saveToDatabase(editableObj,column,id) {
  $(editableObj).css("background","#FFF url(loaderIcon.gif) no-repeat 
  right");
  $.ajax({
    url: "functions.php",
    type: "POST",
    data:'column='+column+'&editval='+editableObj.innerHTML+'&id='+id,
    success: function(data){
      $(editableObj).css("background","#FDFDFD");
    }        
   });
}

show.js: (inspired by this answer)

$(".tbl tbody").on("click", "tr", function() {
  var id = $(this).find("td")[0].text(); // gets the first td of the 
  clicked tr
  var value =  $(this).find("td")[1].text()
  $.ajax({
    url : "table.php",
    dataType: "text",
    success : function (data) {
        $(".day-data").html(data);
     },
     error: function (data) {
        (".tbl").html('No such file found on server');
     }
    });
  });

When user clicks on HTML-table left column it is higligted well; when he changes it, data is addiing to database well. Now when page is refreshed new data is calculated, added to database and shown in HTML-table's right column.

I suppose problem is in show.js. Need some help in correcting this script!

Update1: Added illustartion of my task's logic: