slith

From what I understand.

1) If by “widget” you are referring to a WordPress widget, you cant do this. With page caching the wordpress engine is totally bypassed.

However, if you can modify the widget code, you can do something like this:

<!-- mfunc echo "This is the time not cached " . time(); --><?php echo "This is the time cached" . time(); ?><!-- /mfunc -->

More info: http://www.lost-in-code.com/platforms/wordpress/w3tc-fragment-caching-mfunc

3)

You can do something like this in your functions.php

add_action('wp_head', 'define_if_page_cache');

function define_if_page_cache() {
    if (is_category("News")) {
        define('DONOTCACHEPAGE', true);
    }
}