Advisor is moving. Issues with quitting PhD and settling for a MSc
Honesty is the best policy. It means you should not lie. It does not mean you must say everything about yourself on your resume. For example, you do not need to say where you attended high school on the resume. If you do not have PhD, do not say you have it. If you have MSc, say you have it. You do not need to say you were doing PhD unless they ask you that question.

If and when they ask you whether you were doing PhD, you should tell the truth with brief explanation why you did not get it. This will hurt your chance getting an academic job. Most industry people would not care that much. They are more concerned with your ability to make money. However, you probably will not get an industry job if PhD is part of job requirement.(Some companies do want PhD only)

You need to ask the international student office at your school or immigration office to see the requirement for F-1 visa. They are the authority to answer that question. We are not.

Internship is always helpful. You gain experience which you can put on the resume.