Here's what's happening with your site. First, the reason that none of the players from WP Admin > Settings > TubePress are getting invoked is that, by default, TubePress's WordPress widget will use the following shortcode:
[tubepress resultsPerPage="3" views="false" description="true" thumbHeight="105" thumbWidth="135" theme="sidebar" descriptionLimit="50" playerLocation="popup"]
The result is that these settings are "overriding" the global TubePress settings. The solution is to simply edit the options for the TubePress widget via WP Admin > Appearance > Widgets. Click the TubePress widget and you can change the shortcode. e.g. you might want to use
[tubepress playerLocation="shadowbox" resultsPerPage="6"]
Does that make sense?
As for the Fancybox issue, this is a know bug. The workaround is to either disable the "fancybox-for-wordpress" plugin, or to use a TubePress player location other than Fancybox (I recommend Shadowbox).
What do you think?