First, regarding TOEFL: If the adcom cites a certain minimum score as a requirement – it’s a requirement, not a suggestion or a desired target score. Yet many top MBA programs don’t specify a required minimum score. So while your score may be lower than their average, you can still be a qualified applicant with the current score if other elements of your application are favorable and competitive.
Overall, I’d consider your
list of schools reasonable – it contains some reasonable reaches such as Tuck (a pretty high reach as 670 is low for them, but you bring some clear differentiating strengths, such as your nationality and your work experience) and Tepper; and on-pars such as Madison and Owen.
To answer your questions:
1) It’s possible it could deter you, but it won’t necessarily deter you, as long as the programs you’re applying to don’t require a minimum score higher than 93. So don’t apply to schools that state a minimum score of 100, if they consider it a requirement. For other programs, do everything you can in your application to demonstrate strong English capability.
2) YES!!!
3) No. If you decide to retake
the GMAT and score higher, once you have the score, that’s the time to ask the schools if they will consider your new score (some may, some may not).