NIT

As per the information bulletin, JEE Mains April 2020, there is no such relaxation of marks for Kashmir Migrant. Hence, you need minimum 75% marks at 12th level for admission in NIT and IITs.

You have not written about the home state and category you belong to . However, your expected JEE Mains AIR is above 35000, which is not enough for getting admission in NITs. The ranks below 9000 can be safe for B.Arch admissions.

For NITs like Allahabad Bhopal Jaipur Surat you need atleast 255+. Or else such as Nagpur Delhi and Kurukshetra, the score should be 235+.

Yes, almost every NIT offers courses at undergraduate level in mechanical engineering branch. The admissions to various NIT's are based on the rank scored in JEE Mains examination that will be declared by NTA. Best wishes to you.

Your expected JEE Main AIR is about 132601. Please write about your home state and category you belongs for more better response. However, if you belongs to general category, you can get the following NITs under other state quota (Female).
1. NIT Arunachal Pradesh
2. NIT Manipur
3. NIT Meghalaya.