H1B extension denied, applying for F1 VISA to do PhD. Have questions in DS 160 form

[HolaHola]

I was in US till Jan 2018 with H1B status, my H1B extension I129 petition was rejected on end of December 2017 and I left US on January 2018. I also happen graduate on Dec 2017 with a masters degree and got admitted to an university to pursue my PhD which I am planning to start from Fall 2018. At present I am in the process of filling DS 160 form and I am concerned about couple of questions in the form.

1. Have you ever been refused a US VISA? - Since my extension petition I129 got rejected by USCIS should I say "Yes" to this question? please help

2. Have you ever been unlawfully present, overstayed the amount of time granted by an immigration official or otherwise violated the terms of a US VISA? - Since my H1B extension petition was denied on Dec 2017 and I left US on Jan 2018 should I assume that my stay between this period is unlawful? If yes should I say ?Yes? to this question? Please let me know the consequences.

In one of your DS160 forum it has been mentioned if I say yes to some of the questions the VISA officer will deny the VISA for sure. Please clarify.

[kary151621]

F1 visa for second masters

I have completed my Bachelors in Pharmacy from Mumbai, India in 2011. I worked for 1 year and later went on to study my Masters in Regulatory Affairs from Northeastern University Boston, in June 2013. I have studied and stayed in US from 17th June 2013 to 15 th Aug 2016 in Boston on an F-1 visa including the 12 months OPT. My course started on July 1st 2013 and ended on 27th March 2015 post that I was on OPT. My company had filed my H1b visa and I got a reject on 27th June 2016. In the meantime, I had applied for a course in Project Management at Harrisburg University in Penn for which I got an admit. However, I did not transfer my Sevis within 60 days of OPT end and so had to return to my home country for visa stamping. On return I appeared for visa on 22 nd October 2016 and I got a rejection slip stating potential immigrant after that I never applied for any US visa. I now got an admit from University of New Hampshire for a full time, 12 month on campus Business Administration program for Fall 2018 sem. Is there a way I can get this F-1 visa without being considered as a potential immigrant? What are the steps I need to consider and how should I go about applying for an F1 visa?