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This thread is resolved. Here is a description of the problem and solution.
Problem: Custom template for custom post type does not load posts using get_term() function.
Solution: The problem was that while the taxonomies had been translated, the posts for the custom post type had not translated. If you don't want to translate the posts, set them as "Translatable - use translation if available or fallback to default language" in WPML -> Settings -> Post Type Translations.