How to have exposed filters not displayed on search results
This is pretty simple to do with a little coding:

First create a "Display output" template inside your theme folder that will only target the relevant view (check options using "Theme: Information" bottom right under "Advanced" when you are on your view administration page). Copy the contents of "views-view.tpl.php" inside the file and clear the caches.

After that modify the original filter output:

&lt;?php if ($exposed): ?&gt;
  &lt;div class="view-filters"&gt;
    &lt;?php print $exposed; ?&gt;
  &lt;/div&gt;
&lt;?php endif; ?&gt;


to what you need:

&lt;?php if ($exposed): ?&gt;
  &lt;div class="view-filters"&gt;
    &lt;?php if (!isset($_GET['something'])): ?&gt;
    &lt;?php print $exposed; ?&gt;
    &lt;?php else: ?&gt;
    &lt;?php print l(t('Back to search'), $_GET['q']); ?&gt;
    &lt;?php endif; ?&gt;
  &lt;/div&gt;
&lt;?php endif; ?&gt;


You will just have to replace "something" inside that $_GET to a value that is actually used in your filters (check the URL when you have a search performed - it will look like example.com?something=value1&amp;somethingelse=value2). Since views adds all the filter keys to the URL when a search if performed you can pick any of them.