I found out how to delete a row with this jQuery code. While clicking on a td with the class delete and a garbage icon.
HTML
<table id="foo" class="display" cellspacing="0" width="100%">
<tbody>
<tr>
<td>Foo1</td>
<td>Foo2</td>
<td>Foo3</td>
<td class="delete">IMAGE src here</td>
<td><img src="http://placehold.it/20x20"></td>
</tr>
</tbody>
JAVASCRIPT
$('#foo tbody').on( 'click', 'tr .delete', function () {
$(this).closest('tr').fadeOut("slow", function(){
$(this).remove();
})
} );
But I did not find anything about duplicating rows. I just want to click on a td with another icon in it and the row is duplicated below.