Hello,
There is no particular NRI Quota rather it is NRI category so you can apply for AIQ counselling . It itself means all India so yes you can apply for more than one state. USA schools do not issue transfer certificates but it is needed for admission in India so instead you can ask for a letter which would act as a equivalent to transfer certificate. You do not need 6th to 8th marksheet . Mostly the 12th standard marksheet works fine. And the letter would itself testify that you completed your education till 12th standard.
Hope it helps.
Good luck.
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