A Likert scale - in which a question is posed that is answered on a scale of 1-5 (the most common range) or 0-10 (in the case of the NPS question) - is an easy way to standardize the outcome of a research process and produces a hard number you can do fun things with, like take an average, find the median, or plot pretty graphs. Should you try to include some of these questions when you sit down to run a face to face detailed interview?
The answer is emphatically a No. To get the most learning out of an interview, use open-ended questions to get open-ended responses.
Closed-end questions requiring yes-no answers or multiple-choice answers will cut the conversation short and reduce the potential learnings from the interview.
As a general rule of thumb, face to face conversations should involve open-ended responses, so the subject can tell you what you never would have thought to ask. Online surveys should involve close-ended responses so you have a good way to tabulate responses.
Special thanks: Martin Trust Centre, MIT
Edit: Javier Rojas, 12/05/20