Yes,

You can as long as you either fulfill the domicile criteria of the respective state or have done 11th 12th studies from the other state.
You can apply for private medical institutes throughout the country as the seats are open for all but the fee ranges from 10-20 lakhs per annum.

You can use careers360 college predictor to know the colleges you can get at your NEET score:- https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer