I would like to know what checkboxes i have to check in order for a user to be able to translate content like products, posts etc
Solution: You can set your post types to be translatable at WPML -> Settings in the post type section. Then make sure the user is added as a translator and you can send translations via WPML -> Translation Management. Here is a list of the WPML capabilities, and you can assign whichever ones you would like your Shop Manager to have. https://wpml.org/documentation/support/wpml-admin-capabilities/