Make a selectable list also sortable

Question 1

You probably cannot do both combined as both sortable and selectable is on the same click event, instead just give a holder to sort.

$('#selectable').sortable({ handle: ".holder" })//Make sortable on the handle
  .selectable({
    start: function(event, ui) {
        $currentlySelected = $('#selectable .ui-selected');
    }
    ,cancel: ".holder" //Cancel selection for holder
    ,
    stop: function(event, ui) {
        for (var i = 0; i < selected.length; i++) {
            if ($.inArray(selected[i], $currentlySelected) >= 0) {
              $(selected[i]).removeClass('ui-selected');
            }
        }
        selected = [];
    },
    selecting: function(event, ui) {
        $currentlySelected.addClass('ui-selected'); // re-apply ui-selected class to currently selected items
    },
    selected: function(event, ui) {
        selected.push(ui.selected); 
    }
}).find( "li" )
        .addClass( "ui-corner-all" )
         .prepend( 
             $('<div/>',
                 {'class':'holder'} )
            .append(
                 $('<span/>',
                     {'class':'ui-icon ui-icon-transfer-e-w'})
                  )
             );//Just prepend handle to li's or just addthem in your html itself and remove this section.

Fiddle

You can use this Jquery UI Icons to give whichever icon you want if you are not going with your own.

Question 2

Here is my workaround for making a list selectable and sortable and allows for lasso implementation. Here is the fiddle.

<html>
<meta charset="utf-8" />
<title>jQuery UI Sortable with Selectable</title>
<link rel="stylesheet" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />
<script src="http://code.jquery.com/jquery-1.9.1.js"></script>
<script src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>
$(function() {
//

$('body').selectable({
    filter: 'li'
    //filter: '#album2 > li'
});

/*
Since the sortable seems unable to move more than one object at a 
time, we'll do this:

The LIs should act only as wrappers for DIVs.

When sorting a LI, move all the DIVs that are children of selected 
LIs to inside the sorting LI (this will make them move together);
but before doing that, save inside the DIVs a reference to their
respective original parents, so we can restore them later.

When the user drop the sorting, restore the DIVs to their original
parent LIs and place those LIs right after the just-dropped LI.

Voilá!

Tip: doesn't work so great if you try to stick the LIs inside the LI
*/

$('.connectedSortable').sortable({
    connectWith: ".connectedSortable",
    delay: 100,
    start: function(e, ui) {
        var topleft = 0;

        // if the current sorting LI is not selected, select
        $(ui.item).addClass('ui-selected');

        $('.ui-selected div').each(function() {

            // save reference to original parent
            var originalParent = $(this).parent()[0];
            $(this).data('origin', originalParent);

            // position each DIV in cascade
            $(this).css('position', 'absolute');
            $(this).css('top', topleft);
            $(this).css('left', topleft);
            topleft += 20;

        }).appendTo(ui.item); // glue them all inside current sorting LI

    },
    stop: function(e, ui) {
        $(ui.item).children().each(function() {

            // restore all the DIVs in the sorting LI to their original parents
            var originalParent = $(this).data('origin');
            $(this).appendTo(originalParent);

            // remove the cascade positioning
            $(this).css('position', '');
            $(this).css('top', '');
            $(this).css('left', '');
        });

        // put the selected LIs after the just-dropped sorting LI
        $('#album .ui-selected').insertAfter(ui.item);

        // put the selected LIs after the just-dropped sorting LI
        $('#album2 .ui-selected').insertAfter(ui.item);
    }
});




//
});


<style>
*,
*:before,
*:after {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}

#album {
    list-style: none;
    float: left;
    width: 20%;
    border: 1px solid blue;
}
#album2 {
    list-style: none;
    float: left;
    width: 20%;
    border: 1px solid blue;
}
#album li  {
    float: left;
    margin: 5px;
}

#album2 li  {
    float: left;
    margin: 5px;
}


#album div {
    width: 100px;
    height: 100px;
    border: 1px solid #CCC;

    background: #F6F6F6;    
}
#album2 div {
    width: 100px;
    height: 100px;
    border: 1px solid #CCC;

    background: #F6F6F6;    
}
#album .ui-sortable-placeholder {
    border: 1px dashed #CCC;
    width: 100px;
    height: 100px;
    background: none;
    visibility: visible !important;
}
#album2 .ui-sortable-placeholder {
    border: 1px dashed #CCC;
    width: 100px;
    height: 100px;
    background: none;
    visibility: visible !important;
}

#album .ui-selecting div, 
#album .ui-selected div {
    background-color: #3C6;
}

#album2 .ui-selecting div, 
#album2 .ui-selected div {
    background-color: #3C6;
}

#anotheralbum {
    list-style: none;
    float: left;
    width: 20%;
    height: 800px;
    border: 1px solid green;
}
</style>


<body>

<ul id="album" class="connectedSortable">
    <li id="li1"><div>1- First</div></li>
    <li id="li2"><div>2- Second</div></li>
    <li id="li3"><div>3- Third</div></li>
    <li id="li4"><div>4- Fourth</div></li>
    <li id="li5"><div>5- Fifth</div></li>
    <li id="li6"><div>6- Sixth</div></li>
    <li id="li7"><div>7- Seventh</div></li>
    <li id="li8"><div>8- Eighth</div></li>
</ul>

<ul id="album2" class="connectedSortable">
    <li id="li1"><div>1- 1</div></li>
    <li id="li2"><div>2- 2</div></li>
    <li id="li3"><div>3- 3</div></li>
    <li id="li4"><div>4- 4</div></li>
    <li id="li5"><div>5- 5</div></li>
    <li id="li6"><div>6- 6</div></li>
    <li id="li7"><div>7- 7</div></li>
    <li id="li8"><div>8- 8</div></li>
</ul>
<div id="anotheralbum" class="connectedSortable">
another album - no style for the lists inside here
</div>

<br style="clear:both">
</body>
</html>