WordPress doesn't have a single native place to add tracking scripts, so most sites use either a small header/footer plugin or a direct theme edit. Either path takes a couple of minutes and applies sitewide, including WooCommerce pages.
No — page caching plugins cache your HTML, not third-party script execution, so the script tag ships with the cached page and runs normally in the visitor's browser. If you use an aggressive JS-minify/combine setting, exclude Orbit's script from it to be safe.
Yes — as long as the header code loads sitewide (which header/footer plugins do by default), Orbit tracks WooCommerce cart and checkout pages the same as any other page.
If WordPress only powers the backend and a separate frontend renders pages, header.php and header-injection plugins won't apply — add the script to that frontend's own head template instead.
No — multiple analytics scripts can run on the same page without conflict. You'll just be tracking the same traffic in more than one system.