When you edit your fields, in Advance Settings, you can find a checkbox to enable/disable localization, you can do it also manually in the content type json file at api folder. Unfortunately, right now it does not work with relationship fields.
Yeah, the slug field is also localized, it means you must put a slug for each localized page, it is because you are creating a new page for the same initial page (somehow linked) instead to add additional fields to the same page.