Don't want to make comments on other items as I am not familar with IIT.
For item 3, F-1 holder can legally stay at US up to 14 months, 12 month OPT + 2 month grace period, after graduation. As there might be a gap between graduation and the date when OPT starts, the entire time frame could be slighterly longer than 14 months.
Of course, if you really want to stay in the US and you cannot find a job during OPT, well, now, it also subjects to the quote, you can try to transfer to another school to keep your F-1. However, in this case, if you keep the same Master's level, you cannot get another OPT after you graduate from your second Master's degree.
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