Yes, strings from the theme and Core come to different places on the site. For example, My account element (Header builder) https://gyazo.com/53f8479da033add592d7d5b4eff80929 was coded in the Core plugin that means that translation should be done for the Core plugin. My account page is re-written the default WC template via our theme, so strings of the page are placed in the theme, and so on.
One standard license is valid only for 1 project. Running multiple projects on a single license is a copyright violation.