Colleges in Rajasthan

Check this link:
http://www.bits-pilani.ac.in/university/wilp/wilpoverview

I think you can do that but for this check with the college once.

Dear,
In Rajasthan, under RTU affiliated colleges, the fees is 70000/per year. But Anand International College of Engineering provides meritorious scholarship with all the apparatus in mechanical labs in ME. So, the further process to get admission, please visit the college's website.
Best wishes for

B.Sc in aviation science costs Rs.20 lakhs for 3 years in Banasthali.
And, as for the early installments, they vary.

It depends upon the branches.

No, there is no such thing in BITS.

It's worth doing it. To know more about it, check the following links:
http://www.bits-pilani.ac.in/pilani/management/management
https://www.facebook.com/MBA.BITS.Pilani/?ref=br_rs

Law from Banasthali Vidyapeeth would be the best among the options you have.

Yes, the quality of education in Banasthali is quite good. Banasthali emphasis on 5 fold education of girls. After studying in Banasthali, you can find good placement opportunities across India.