One means to do this is:
$(document).ready(function() {
$('body').on('click', '.AddEl', function() {
$('.actions:first')
.parent()
.clone()
.attr('id', 'element_' + $('.actions').length)
.insertAfter($('.actions:last').parent());
});
$('body').on('click', '.RemoveEl', function() {
$(this).closest('.actions').parent().remove();
});
});
JS Fiddle demo.
Please note that I've amended your html so that the first element to be cloned is now id="element_0", and targeted that, and all subsequently-created elements, with the CSS selector:
div[id^=element] {
/* css */
}
This could be simplified, but these are simply my first thoughts.
Edited to offer a slightly improved version, in that the initial addition is slightly, or seems a little, more concise, and also features a means to prevent duplicate ids being generated if elements are added/removed:
$(document).ready(function() {
$('body').on('click', '.AddEl', function() {
var $elems = $('.actions').parent();
$elems
.first()
.clone()
.insertAfter($elems.last());
$('div[id^="element_"]').each(
function(i){
$(this).attr('id','element_' + i);
});
});
$('body').on('click', '.RemoveEl', function() {
$(this).closest('.actions').parent().remove();
});
});
JS Fiddle demo.