Problem: I would like to include Types custom field values from my custom post type in REST API queries.
Solution: You can expose custom field values in standard post reponses in the REST API by turning on the REST setting in Toolset > Settings > Custom Content. In other custom API endpoints, you may need to register each custom field using the register_api_field API and get_post_meta (raw field values) or types_render_field API (formatted field values).
Problem:
The user would like to assign some taxonomy terms, to a post created using a Toolset form, automatically.
Solution:
The code that you shared seems to create a Reg User post. If you want to create a taxonomy term, you will need to use the function wp_insert_term. And if you want to assign the taxonomy term to the post, you can use the wp_set_object_terms function.
To get the value of the field, use the get_post_meta function or you can use the $_POST array data. You may need to add the wpcf- prefix to the field slug.