Welcome to WPSE. This is a rather broad question and perhaps not quite on topic here, but here are some links that should get you started developing a solution to match your needs.
- Introduction to Plugin Development – A custom plugin is good place for this kind of custom functionality so it won’t be lost if/when you change theme on your site.
- Use register_post_type() to register your custom post type.
- Use wp_insert_post() to save new post entries to the database.
- REST API Handbook – You might need to register one or more custom REST endpoints, for example to handle the suggestions loading and saving the user submitted data, depending on how you implement the address form.