Manipulating Drag and Drop values sortable with Jquery

Question

Picture scheme:

Problems:

• Order and quantity of the boxes of first column should not be changed. I could not leave them only for the purpose of DRAG, I mean, I can’t remove a box from the second and go back to the coluna 1, but between the day of the week columns and without generating copies.

• I need every day, SEGUNDA, TERÇA, QUARTA... are limited according to the rule shown in the image (check attachment). The order of the boxes does not matter for each day. What matters is the limit. Exemplo: Never in a day should one have two box that are worth one expedient.

• When there are two clicks on the boxes that are on the day of the week, the box should disappear and this happens, but with a mistake. I can’t delete more than one box with the same class.

• The big challenge is QUARTA CAIXA. It can be placed boundlessly over any box limit within days, i.e.: **On the second I can add SOMENTE CAIXAS DO TIPO 4**.

• EXTRA: how could I see AJAX, save these values to a database table? Put inputs instead of divs? Create a form? Or there is a way to detect the click of a button and capture the information of each id="seg", id="ter", etc...?

WHAT I ALREADY HAVE

        var sum = 0;

		$('.nip').sortable({
		    revert: 'invalid',
		    connectWith: '.nip',
		    forcePlaceholderSize: false,
		    helper: function(e,li) {
		        copyHelper= li.clone().insertAfter(li);
		        return li.clone();
		    },  
		    stop: function(){
		        // habilitando todos os sortables
		        $('.nip').each(function(){		        	
		            var $this = $(this);
		            sum = parseFloat($(this).text());  //ou this.innerHTML, this.innerText
	         		console.log('SUM: '+ sum);
		            $this.css('borderColor','gray');
		            $this.sortable('enable');
		        });
		    }
		});

	  	/* AQUI ELE REMOVE, MAS REMOVE SOMENTE UM */
		$('ul.ui-sortable li').dblclick(function() {
		    $(this).remove();
		  });


		$('.nip li').mousedown(function(){
		    // Verifique o número de elementos no sortable
		    $('.nip').not($(this).parent()).each(function(){
				var $this = $(this);
				
		        if($this.find('.drag').length >= 4){
		            $this.css('borderColor','red');
		            $this.sortable('disable');
		        } else {
		            $this.css('borderColor','gray');
		            $this.sortable('enable');
		        }
		    });
		})

		
	.nip { display:inline-block; margin:5px; border:1px solid grey; vertical-align:top; }
	.nips { display:inline-block; margin:5px; border:1px solid grey; vertical-align:top; }
	ul { min-width:100px; min-height:60px; }

	li.um { color: #fff; background-color: red; text-align: center; padding: 60px 20px 20px 20px; width:50px; height:60px; margin:5px; border:1px solid silver; }

	li.dois { color: #fff; background-color: blue; text-align: center; padding: 30px 20px 20px 20px; width:50px; height:30px; margin:5px; border:1px solid silver; }

	li.tres { color: #fff; background-color: green; text-align: center; padding: 20px 20px 20px 20px; width:50px; height:15px; margin:5px; border:1px solid silver; }

	li.quatro { color: #fff; background-color: black; text-align: center; padding: 10px 20px 20px 20px; width:50px; height:7px; margin:5px; border:1px solid silver; }

	.semana{
	    width: 960px;
	    margin: 0 auto;
	}

	.caixa{
	    float: left;
	}

	.caixa p{
		font-family: arial;
	    padding: 10px;
	    text-align: center;
	}

	#drags{float: left;}

<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.9/jquery-ui.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.5.2/jquery.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<link rel="stylesheet" href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.3/themes/smoothness/jquery-ui.css">
<link rel="stylesheet" href="http://fiddle.jshell.net/css/normalize.css">
<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.3/jquery-ui.min.js"></script>

	<ul class='nip' id="drags">
	    <li class="um">1</li>
	    <li class="dois">2</li>
	    <li class="tres">3</li>
	    <li class="quatro">4</li>
	</ul>

<div class="semana">
	<div class="caixa">
		<p>SEGUNDA</p>
		<ul class='nip' id="seg"></ul>
	</div>
	
	<div class="caixa">
		<p>TERÇA</p>
		<ul class='nip' id="ter"></ul>
	</div>
	
	<div class="caixa">	
		<p>QUARTA</p>
		<ul class='nip' id="quar"></ul>
	</div>

	<div class="caixa">
		<p>QUINTA</p>
		<ul class='nip' id="quin"></ul>
	</div>
	<div class="caixa">
		<p>SEXTA</p>
		<ul class='nip' id="sext"></ul>
	</div>

	<div class="caixa">
		<p>SÁBADO</p>
		<ul class='nip' id="sab"></ul>
	</div>

	<div class="caixa">
		<p>DOMINGO</p>
		<ul class='nip' id="dom"></ul>
	</div>
</div>