Correct me if I'm wrong:
You say that the post can be seen only by direct link. Also, that post is not appearing on the front page and also, is not appearing on the widget under "Latest" tab.

Here is what I see: That post is 7'th post on the front page (you can see that even on the picture attached on my previous message). I have clicked on post's link and everything seems to work normally.
On the "Latest" tab, that post is not appearing because the limit of showing posts is 5. Therefore, that post could not be on the "Latest" tab, because is the latest 7'th post.

Change the post date of The Time Management Game | Chrono Sapien | Intelligent Time Management
Log in to your wordpress dashboard and go to Posts -> All Posts.
Hover the post title The time Management Game and choose Quick Edit.
Then, change the Date to today's date and click on Update button.
Also, don't forget to empty the cache if you have some cache plugin installed (like W3 Total Cache or Wp Super Cache).
All posts are displayed in descending order based on date. The last post (one with the yellow book) was posted on November 27, 2013. The post in discussion was posted on November 11, 2013.

Hope it will help.

Sure..

Index.php:

<?php
/**
* Index Template
*
* The index template is a placeholder for all cases that don't have a template file.
* Ideally, all fases would be handled by a more appropriate template according to the
* current page context (for example, `tag.php` for a `post_tag` archive or `single.php`
* for a single blog post).
*
* @package WooFramework
* @subpackage Template
*/

get_header();
global $woo_options;
?>
<!-- #content Starts -->
<?php woo_content_before(); ?>
<div id="content" class="col-full">

<div id="main-sidebar-container">

<!-- #main Starts -->
<?php woo_main_before(); ?>
<div id="main" class="col-left">

<?php get_template_part( 'loop', 'index' ); ?>

</div><!-- /#main -->
<?php woo_main_after(); ?>

<?php get_sidebar(); ?>

</div><!-- /#main-sidebar-container -->

<?php get_sidebar( 'alt' ); ?>

</div><!-- /#content -->
<?php woo_content_after(); ?>

<?php get_footer(); ?>



and I can't see a front page template, just a page one:

<?php
/**
* Page Template
*
* This template is the default page template. It is used to display content when someone is viewing a
* singular view of a page ('page' post_type) unless another page template overrules this one.
* @link Pages « WordPress Codex
*
* @package WooFramework
* @subpackage Template
*/

get_header();
?>

<!-- #content Starts -->
<?php woo_content_before(); ?>
<div id="content" class="col-full">

<div id="main-sidebar-container">

<!-- #main Starts -->
<?php woo_main_before(); ?>
<div id="main">
<?php
woo_loop_before();

if (have_posts()) { $count = 0;
while (have_posts()) { the_post(); $count++;
woo_get_template_part( 'content', 'page' ); // Get the page content template file, contextually.
}
}

woo_loop_after();
?>
</div><!-- /#main -->
<?php woo_main_after(); ?>

<?php get_sidebar(); ?>

</div><!-- /#main-sidebar-container -->

<?php get_sidebar( 'alt' ); ?>

</div><!-- /#content -->
<?php woo_content_after(); ?>

<?php get_footer(); ?>

No, you can't see the post through direct link if the post was saved as draft. Have you tried this? Because I'm working right now on a wp based website and I couldn't reach the post (previously saved as draft) by direct link.

Maybe the RSS software you use is retrieving the post's date from the website you use as source and publish all posts on your website with the date retrieved from that RSS source.