Fancybox popup once time for session

Question 1

For browser consistency, you may need to delay the fancybox load execution for the first time so try this code :

function openFancybox() {
    // launches fancybox after half second when called
    setTimeout(function () {
        $('#yt').trigger('click');
    }, 500);
};
$(document).ready(function () {
    var visited = $.cookie('visited'); // create the cookie
    if (visited == 'yes') {
        return false; // second page load, cookie is active so do nothing
    } else {
        openFancybox(); // first page load, launch fancybox
    };
    // assign cookie's value and expiration time
    $.cookie('visited', 'yes', {
        expires: 7 // the number of days the cookie will be effective
    });
    // your normal fancybox script
    $("#yt").click(function () {
        $.fancybox({
            // your fancybox API options
        });
        return false;
    });
});

See code at this JSFIDDLE

NOTES :

In order to see the cookie working, you may need to use jsfiddle's full screen mode http://jsfiddle.net/aVE9N/show/
I would advice you to update (at least) your fancybox version from v1.3.1 to v1.3.4
It's assumed you are loading properly the jQuery cookie plugin in your page

Question 2

Using the jQuery cookie plugin you suggested:

$(document).ready(function() {
    if(typeof $.cookie('popupVideoPlayed') == 'undefined') {
        $.cookie('popupVideoPlayed', 'true'); // set a session cookie so it won't play again
        $('#yt').trigger('click');
    }
});

Remember to delete the inline body onload event handler.

Question 3

¡UPDATED!

If you're using the newest JavaScript Cookie plugin this is for you:

HTML

<a class="c-p" href="#cookies" style="display: none;">Inline</a>
<div id="cookies" style="display: none;">
    <p>Lorem ipsum dolor sit amet consectetur adipisicing elit. Dignissimos rem nulla quae dolorum omnis possimus, ducimus nisi pariatur harum debitis quo, excepturi nam ratione modi. Architecto, enim. Amet, saepe mollitia?</p>
</div>

JavaScript

function openFancybox() {
    setTimeout( function() {jQuery('.c-p').trigger('click'); },1500);
}
jQuery(document).ready(function() {
    if (Cookies.get('visited')) {
        return false;
    } else {
        Cookies.set('visited', 'no', { expires: 7 });
    } 
    if (Cookies.get('visited') == 'yes') {
        return false;
    } else {
        openFancybox();
        Cookies.set('visited', 'yes');
    }
    jQuery('.c-p').fancybox();
});

Note: I implemeted it in my custom WordPress theme and it worked perfectly.