You should not have html elements in table directly rather you need to put them in some td. The html should be changed. You can add hidden field in the same row in new td after your .deleteME.
Html
tr>
<td class='headline2' style="width: 200px; padding-bottom: 20px; padding-top:20px; padding-left: 10px; text-align: left;"><?= $value['f_name'] . " " . $value['l_name']; </td>
<td class='headline2'><?= $value[0]->end ?><br><?= $value[0]->start ?></td>
<td class='headline2'style='padding-right:18px;'><?= $value[0]->updated ?></td>
<td><div class="approve"><input disabled <? if ($value[0]->studentApproved == 1) { ?>checked<? } ?> type="checkbox"><label><span></span></label></div></td>
<td><div class="approve"><input disabled <? if ($value[0]->companyApproved == 1) { ?>checked<? } ?> type="checkbox"><label><span></span></label></div></td>
<td><div class="approve"><input class="approveME" value="<?= $value[0]->application_id ?>" <? if ($value[0]->koordinatorApproved == 1) { ?>checked<? } ?> id="<?= $i ?>" type="checkbox"><label for="<?= $i ?>" ><span></span></label></div></td>
<td><input class="deleteME "type="image" src="../wp-content/themes/tutorial_theme/images/DELETE.png"><td>
<td>
<input class="hidden" value="<?= $value[1] ?>">
<input class="hidden" value="<?= $value[0]->user_id ?>">
</td>
</tr>
Javascript
var class_id = $(this).closest('tr').find('.hidden:eq(0)').val();
var user_id = $(this).closest('tr').find('.hidden:eq(1)').val();
Or
var class_id = $(this).parent().next('td').find('.hidden:eq(0)').val();
var user_id = $(this).parent().next('td').find('.hidden:eq(1)').val();