How to control a taxonomy view's output?
It sounds like you're trying to do a couple complex things: 1) use contextual filters to choose which term to show and 2) then you're trying to theme certain taxonomy term pages. Once you've got stuff set up in a way that uses these concepts, you should be able to accomplish your end goal (But the views need to be dynamic, so that if a new type/application is used, it is added to the list to the left and the styles applied as desired.) relatively easily.

This is a good basic introduction into Views Contextual Filters: http://www.metaltoad.com/blog/using-drupal-contextual-filters-views

As for theming taxonomy term pages, I think everyone has different ideas on how to best to do that, but if you've already got these three views set up, it might be easiest to use Panels (https://drupal.org/project/panels) and drop those existing views into a panel that is context-based. Of course, Panels comes with its own learning curve, so it might not actually be that easy (though here is a basic introduction for something like what you're trying to do: https://drupal.org/node/1582906). And maybe I'm over-complicating this by assuming you want to theme your pages; maybe contextual filters were all you needed?

Just in case, here are some other ways of theming taxonomy pages:


override taxonomy-term.tpl.php (the basics of overrides: https://drupal.org/node/173880)
Display Suite: https://drupal.org/project/ds


I'm sure there are a bunch of other ways too, but that's all I've got off the top of my head for now. And I'm sure someone else will chime in with more options soon.

Also, here are some other links that you might find useful: 


How to theme each nodes in a taxonomy term page seperately in drupal 7
Theme a taxonomy terms page
Overriding the default taxonomy page with a view in Drupal 7