WooCommerce: I Need to hide my page title/header (including menu) from all the WooCommerce related product pages, such as category and keyword pages

Take a look at the body class tags. This will help you further define your CSS selectors to target the elements you want to hide. In this use case, you can a single CSS rule to hide the header on each and every woocommerce page.

Here is what I would use in your case
.woocommerce header{ display: none; }

There are many different ways to do this. You could use PHP or Javascript to accomplish the same results but I believe this is the simplest solution.