Always put your output div outside the form and your javascript. In this format. 
<script src="jquery.js" type="text/javascript"></script>
<script src="jqueryPlugins.js" type="text/javascript"></script>
<div id="mulitplefileuploader">Upload</div>
<form></form>
<script  type="text/javascript"> ... </script>
EDIT:
I've looked at your link. You need to include your validation plugin right at the bottom, this should resolve the conflict. Also I strongly advice to use developer tools in browser. "In Chrome, open developer tools/inspect element - click on console log - you will see where is the conflict." 
<html lang="en"><head>
<meta charset="utf-8">
<link href="uploadfile.css" rel="stylesheet">
<script src="../../js/jquery-1.10.1.min.js"></script>
<script src="jquery.uploadfile.min.js"></script>
</head>
<body>
<form id="form_galerija" action="" method="post" novalidate="novalidate">
    <p><input type="text" name="name" id="name" value="" placeholder="Name..."></p>
    <p><input type="text" name="surname" id="surname" value="" placeholder="Surname..."></p>
    <div id="files">
    </div>
    <p><input type="submit" name="submit_ok" value="Dodaj slike"></p>
</form>
 <script type="text/javascript">
    $(document).ready(function(){
        var validator = $('#form_galerija').validate({
          rules:{
            name:{required:true},
            surname:{required:true}
          },
          messages:{
            name:{required:'Name je obavezan!'},
            surname:{required:'Surname je obavezan!'}
          },
          submitHandler: function(form){
            $('#submit_ok').attr('disabled','disabled');
            $('#submit_ok').attr('value','Pričekajte...');
            $(form).ajaxSubmit({
              url: 'http://www.agroklub.com/test/image3/index2.php',
              success: function(r){
                if (r.match(/true/gi)) {
                    title = $('#name').val();
                    alert('Slika "'+title+'" je uspješno dodana!' + r);
                }
                else {
                    $('#submit_ok').removeAttr('disabled');
                    $('#submit_ok').attr('value','Dodaj slike');
                    alert('Greška prilikom dodavanja slika!' + r);
                }
              }
            });
          }
        });
    });
</script>
    <div class="ajax-upload-dragdrop" style="vertical-align:top;"><div class="ajax-file-upload" style="position: relative; overflow: hidden; cursor: default;">Upload<form method="POST" action="upload.php" enctype="multipart/form-data" style="margin: 0px; padding: 0px;"><input type="file" id="ajax-upload-id-1417544307288" name="slika[]" multiple="" style="position: absolute; cursor: pointer; top: 0px; width: 64px; height: 35px; left: 0px; z-index: 100; opacity: 0;"></form></div><span><b>Drag & Drop Files</b></span></div><div id="mulitplefileuploader" style="display: none;">Upload</div><div></div>
    <div id="status"></div>
<script>
    $(document).ready(function(){
        var broj = 1;
        var settings = {
            url: "upload.php",
            dragDrop:true,
            fileName: "slika",
            multiple:true,
            allowedTypes:"jpg", 
            returnType:"json",
            onSuccess:function(files,data,xhr)
            {
               //alert((data));
               $("#files").append("<input type='text' value='" + data + "' name='file_" + broj + "' />");
               broj++;
            },
            showDelete:true,
            deleteCallback: function(data,pd)
            {
                for (var i=0; i<data.length; i++)
                {
                    $.post("delete.php",{op:"delete",name:data[i]},
                    function(resp, textStatus, jqXHR)
                    {
                        //Show Message  
                        $("#status").append("<div>File Deleted</div>");      
                    });
                }      
                pd.statusbar.hide(); //You choice to hide/not.
            }
        }
        var uploadObj = $("#mulitplefileuploader").uploadFile(settings);
    });
</script>
<script src="../../js/jquery.validate.min.js"></script>
</body></html>