Hi nagi1337,
Thanks for posting your profile. You have a lot of strengths - I like your academic strength (strong grad GPA, solid GRE), robust work experience and trajectory (promotions!), as well as differentiated personal background coming from Pakistan. That said, be sure to explain in your apps why you need an MBA because you already have a Masters in Finance. What specific skillset or knowledge are you seeking at business school that you did not learn at Syracuse?
To answer your questions -
1. Both the GRE and GMAT are accepted by the schools on your list (and most other US business schools). Your current GRE score is competitive, but certainly 330+ would be even more so.
2. I think your profile would be competitive at HBS, Wharton, MIT and Yale. However, these are 4 very selective programs. Are you open to considering other programs? Schools like Booth, Darden, NYU - while not exactly easy - have higher acceptance rates that can help maximize your chances of success.
I hope this is helpful to you. If you would like to discuss your profile in more detail, feel free to schedule a 1:1 consultation with us. Wishing you the best in your MBA journey!
Sincerely,
Debbie