Where can I find the template that is used for the product-category page? The general template is "page-full.php". But where is the template for the single-product page (single.php?) and the product-category page? I'd like to edit them to show elements that are not visible on other pages and vice versa. Much appreciated.
Your theme doesn't necessarily include all these template files.
It might just use
index.php to serve the single page template as well as listings (category, date, author, tag, etc).
If you add a
single.php file, WP will use that instead of
index.php for example.
'product-category.php' (as @ialocin rightly says) is almost certainly a WooCommerce template file and the way you override that is different. They have good docs: http://docs.woothemes.com/document/template-structure/
The general principle is the same - you override the default template (index.php) with successively more-specific templates.