The first issue is resolved. The real problem was that wp_footer() was misplaced after the closing body tag and was causing the issue above.
But the second issue still exists.
I have a custom post named “products”. When I edit a product the cached page of the product (single) is generated successfully but, even though I have enabled to clean archives when a post is edited, the product’s taxonomy page is not cleared. Will the plugin work with custom post types?
Thanks!