IIT

Hello Tripti,
As per your rank, your chances are slim for getting any IIT's,however check here to know more:
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

You can appear for SAT Examination along with JEE provided you can prepare for both exams simultaneously.

IIST, PEC University Chandigarh, Manipal University, Amity University, Anna University etc are good options for doing B.Tech Aeronautical Engineering or Aerospace Engineering based on academic environment and placement records.

Yes, you are eligible but in case of counselling home state candidates are preferred so you should score high marks as you can.

The Indian Institutes of Technology ( IIT) are autonomous public institutes of higher education. IITs are located at Bhilai, Madras, Delhi, Dhanbad, Dharwad, Goa, Guwahati, Jammu, Kanpur, Kharagpur, Bombay, Roorkee, Bhubaneswar, Gandhinagar, Hyderabad, Indore, Jodhpur, Mandi, Palghat, Patna, Ropar,

The OBC CAT cutoff for MBA in IIM Indore is 80 percentile. You can check sectional cutoffs for it as well here: http://www.iimidr.ac.in/academic-programmes/post-graduate-program-in-management/pgp-indore-admissions-details/
For other MBA colleges you can check this detail on their website.

IIT-Bhubaneswar is a new IIT, whereas, Jadavpur is an old established university with excellent track records in academics and campus placement, therefore, it is recommended that you opt for Jadavpur University over IIT-Bhubaneswar.

You need to qualify JEE Mains in order to pursue B.Tech from NIT.

No, it is not mandatory to study in a govt college to get a govt job. You need to concentrate on GATE exam and perform well in it. So start your preparation well before hand.
All the best!

There are 2 ways to become a Govt College Professor :
1.You have to clear the UGC NET or SET/SLET Exams.
2.Other option is,securing a P.hd Degree in your subject.