Hi,
1. Please provide a screenshot of the settings of your filters, a screenshot of the custom fields used by the filters and a link to the page with the filters not working.
That way we'll be able to understand your issue.
Also, this feature is a Business edition feature but I don't see any subscription for the Business edition of HikaShop for your account. I suppose that you must have purchased it with another account. Could you provide your order number ?
2. It's probably because you turned off the "append characteristic value to product name" setting of the HikaShop configuration.
If it's not that, then it usually means that the layout of the product page has been modified incorrectly, breaking the characteristic system.
3. Which invoice are you talking about ? If you want to add the order status in the invoice that you can display from the backend of the website, you can edit the file "invoice" of the view "order" for your backend template via the menu Display>Views and add such code:
<?php echo $this->element->order_status; ?>