It used to be that the I20 would not be issues until you were actually a student and enrolled (not just an admit but actually paid the deposit and enrolled). I have a feeling it is still the same way so the schools are actually encouraging you to enroll.
A good rule is that you need you i20 at least 2 months before arriving. So that should answer your other questions. However you can ask the schools about their specific policies directly and should be able to be very open about them.
Congrats and good luck!
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