List of quick-links:

Question: When navigate out of Virtuemart (For example: to Homepage), there is a blank placeholder for Cherry Picker without filters. How to remove it?

Reason: Joomla always reserves places for all published modules no matter if it's empty or not.
To make sure position is created only when in Virtuemart - do the following:

at your template's index.php first get the values:
<?php $option = JRequest::getString('option', null); ?>

Then do a check if it's Virtuemart (com_virtuemart) and only then publish module into 'display_chp' position. (First add this position to templateDetails.xml)
<?php if ($option == 'com_virtuemart') { ?>
   <jdoc:include type="modules" name="display_chp"/>
<?php } ?>

Question: There are no filters on Homepage. What do I do?

That's correct.
Normally filters appear only in categories when there are actual products to filter.
But you may insist on showing filters on any page you want. Specify at ChP's back-end the Product Type ID filters of which you wish to show. After that just select the pages you want the module to display on.

Question: I want to add a "Reset all filters" button

This is basically a link to a current category. So add this code to any file you wish (whatever part of the site you want it to appear on):

Virtuemart 1.1
$itemid = JRequest::getVar('Itemid', '');
$category_id = JRequest::getVar('category_id', '');

$url='/index.php?option=com_virtuemart&page=shop.browse&Itemid='. $itemid. '&category_id='. $category_id. '&limitstart=0';
echo '<a href="' . $url . '">Reset all filters</a>';
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