Improve Acyba Pop Up Window

Using the Product Insert Pop Up window for HikaShop products I would like to have available in the list only those products that are published.

Is there a parameter that I was not able to find? Should some quary code be changed somewhere?

Also I would like to simplify (reduce) the amount of tabs and options for this Pop Up window as it is too much stuff for the end user of my project. Which files shall I edit?

You need to add the line:
$filters=array('a.product_published=1');

after:
$db = JFactory::getDBO();

in plugins/acymailing/hikashop.php if you only want published products.

Also, to modify the html of the popup, the modifications can be done in that same file, below that piece of code, in the same acymailinghikashop_show function.

About the second point Idon't figure how to do it. Could you explain further? I want to remove the "Coupon Tab".

You can add the code:
echo $tabs->endPane();
return;

before the line:
echo $tabs->startPanel( JText::_( 'COUPONS' ), 'hikashop_coupon');