Do you repeat a mantra given to you by instructor? Yes, the mantra is repeated in your mind, not outwardly.
How did he come up with that? Instructors are trained on how to teach the practice of TM and give each person a mantra based on the person’s age, gender and comfort with the mantra. The mantra will not have specific meaning to you. I have seen mantras listed on the Internet.
Who else is using it (the instructor claims it’s unique, I know)? Actually its not really unique to just you. Others are certainly assigned the same mantra based on criteria above.
Whom are you addressing with your mantra? The mantra is not spoken outloud. You are not addressing any one. It is simply a nonverbal repetition that helps the mind to move away from concentrated thought for a short period of time. You can stop at any time.