Yes, definitely. I use the same exercises for developing a speaking voice or a singing voice. If you are having any problems with your speaking voice, I recommend this technique to help you achieve a clear, resonant sound and a strong connection to your breathing.
Yes, having over 25 years of experience with auditions has given me insights into how to best prepare for them. If you want to work only on audition material for a limited number of sessions, we would skip the technique and focus on your immediate goals.
A voice teacher is someone trained in vocal technique and vocal artistry. A vocal coach is focused primarily on vocal artistry and working with various languages. A coach works minimally with technique and primarily with artistry/languages.