Hi again Dariusz

1. Unfortunately, you will need to add your locale.

This is an example for German/

1. Open ../wp-content/plugins/wpdatatables/assets/js/wpdatatables/wdt.funcs.js and add this code under the comments "Apply datetimepicker" around line 147:

moment.locale('de', {
        months : ["Januar","Februar","März","April","Mai","Juni","Juli","August","September","Oktober","November","Dezember"],
        monthsShort : ["jan", "feb", "mär", "apr", "mai", "jun", "jul", "aug", "sep", "okt", "nov", "dez"],
        weekdaysMin : ["So", "Mo", "Di", "Mi", "Do", "Fr", "Sa"],
        week : {
        dow : 1 // Monday is the first day of the week
        }});

Then, below that find this line of code around line 169:

$(this).datetimepicker(
            {
                format: wdtDateFormat + ' ' + wdtTimeFormat,
                showClear: true,
                keepOpen: true,
                useCurrent: false
            }
        )

And modify it to look like this (add "locale: 'de' "):

$(this).datetimepicker(
            {
                format: wdtDateFormat,
                showClear: true,
                keepOpen: true,
                useCurrent: false,
                locale: 'de'
            }
        )

Do not forget to add a comma ( , ) after " useCurrent: false " (see code above). If you forget that, this will not work.

Then, do the same for around line 183 (add "locale: 'de' "):

$(this).datetimepicker(
            {
                format: wdtDateFormat,
                showClear: true,
                keepOpen: true,
                useCurrent: false,
                locale: 'de'
            }
        )
            .off('dp.show')
            .on('dp.show', function () {
                $(this).parent().find('div.bootstrap-datetimepicker-widget').addClass('wdt-datetimepicker-modal');
                if (!_.contains(['MM/Y','MMM Y','Y'], wdtDateFormat)) {
                    wdtAddDatePlaceholders($(this));
                }
            });
    });

Again, do not forget to add a comma ( , ) after " useCurrent: false " (see code above). If you forget that, this will not work.

2. Open ../wp-content/plugins/wpdatatables/source/class.wdttools.php and around line 1469 add the following line of code:

wp_enqueue_script('wdt-moment-de', WDT_JS_PATH . 'moment/locale/de.js', array(), false, true);

So it should look like this in the end:

wp_enqueue_script('wdt-moment', WDT_JS_PATH . 'moment/moment.js', array(), WDT_CURRENT_VERSION, true);
wp_enqueue_script('wdt-moment-de', WDT_JS_PATH . 'moment/locale/de.js', array(), false, true);
wp_enqueue_script('wdt-bootstrap-datetimepicker', WDT_JS_PATH . 'bootstrap/bootstrap-datetimepicker/

This also changes the date picker starting day, so the week starts from Monday, not Sunday.

3. Open this file: 

wp-content/plugins/wpdatatables/assets/js/wpdatatables/wdt.frontend.min.js

Since this is a minified file, you have to search for the following line of code:

$(this).datetimepicker({format:wdtDateFormat,showClear:!0,keepOpen:!0,useCurrent:!1})

and change it to look like this:

$(this).datetimepicker({format:wdtDateFormat,showClear:!0,keepOpen:!0,useCurrent:!1,locale:'de'})

The last step is to go to the main settings of wpDataTables, under Custom JS and CSS  tab, and disable the "Use minified wpDataTables Javascript" check-box.

2. At the moment, this is the default behavior of the picker, since it's generated from a 3rd party HTML5 library, so we can't change it at the moment, but I will forward this to our developers, so they can work on it in the future.