Engineering

These are the top colleges for pursuing CSE.
Indraprastha Institute of Information Technology, Delhi
Jamia Millia Islamia, New Delhi
Indira Gandhi Delhi Technical University for Women, Delhi
Bhagwan Parshuram Institute of Technology, Delhi

She has a good score. You can check the list of possible colleges here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

You may get admission in some of the private colleges through this score. Check possibilities of getting colleges here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Of course, you can. There are several engineering entrance exams like:
WBJEE, COMEDK, BITSAT, VITEEE, SRMJEE, KIITEE, etc.
You can also consider private colleges in South India that are even better than some government colleges in the north.

You may get admission there but I am not so sure about this. As in 2015, the closing rank for mechanical engineering was 39000 and from 2015, we saw that a gradual decrease in demand of engineering courses it is a point of hope for you. I would suggest you to appear in the counseling and go till the final round. Rather than VITEE, you should try for some other ways too.

I am attaching a link where you will get all the related information to get admission in University of Hyderabad:
https://www.shiksha.com/university/university-of-hyderabad-uoh-23069/admission

You can go for counseling till last round and you may get a lower branch there. Check your possibilities of getting a college here: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

In 2nd and 3rd round you can get colleges like NIT Srinagar, Aizwal, Srinagar, Dimapur and some central universities.

You can consider following colleges:
Sreenidhi Institute of Science and Technology, [SNIST] Hyderabad.Malla Reddy Engineering College, [MREC] Hyderabad.CMR Institute of Technology, [CMRIT] Hyderabad.
Institute of Aeronautical Engineering, [IARE] Hyderabad.