1. Do I have a competitive profile for part-time at NYU & Chicago.
From what you've told me, you'd have a shot, but it certainly won't be easy.
2. Can you suggest any other good schools that I should consider.
Depends on your career goals.
3. I may be getting a good job offer soon and probably will accept that offer. Now, I live and work in NJ. Does it mean that if I enroll in a part-time program, say in Chicago, I have to fly there 2-3 times a month. What would be the best options in such a situation?
If it's a real part-time program you'd have to go much more than that. If you want to attend a part-time, i'd recommend attending one close by.
4. My long term goal is to set-up a specific type of knowledge based company. Do I need to provide some details of this idea on the essays?
Yes. Applicants get dinged all the time, because they simply say that they want to be an entrepreneur, but don't provide any details.
5. Also, I found a current studentâ€™s contact information at that programs website. Is it acceptable to contact this person to get some information about the program?
Some students are designated to answer applicants' questions. If that is this student's role, then feel free. If you're running a google search to get contact info then it's not appropriate.