India

List of the best BBA Aviation Colleges in Bangalore:
Jain University
East Point College, Bangalore
IIMS
BGS Global SJB College Bangalore
Hillside College Bangalore
Brindavan College Bangalore
SJES College Bangalore
East-West College Bangalore
Koshys College Bangalore
Christian college Bangalore
RR College Bangalore.

There are numerous of courses available for B.Tech in India some of the courses are as follows:-
Computer Science
Information Technology
Mechanical Engineering
Electrical and Electronics Engineering
Electrical and Communication Engineering
Electronics System Engineering
Food Technology
Paint Technology
Leather Technology
Plastic Engineering
Textile Technology
Metallurgy engineering, etc.

There are many such colleges which have low fees but their infrastructure, faculty members, facilities etc. Are poor compare to others. However, you can choose that one which has an affordable price or you can go for scholarship exam too for financial support. Many colleges conduct not only entrance exam but scholarship also which is known as entrance cum scholarship exam. By getting higher marks you can get the seat as well as some scholarship also.
Best of luck.

Yes, you can apply for NPTA exam for BBA. It also offers distance learning mode. But for admission, you have to first clear the cut-off of the entrance exam.

Yes, your son can get a seat. But getting a seat in high demand courses like CSE and mechanical engineering is difficult.
Best of luck.

Unfortunately, no. The demand for CSE is higher and it requires at least 98.5% marks or above 150 marks in JEE. Try in other universities.
Good luck.

You can apply through another state quota. For that, you need to have a great score of more than 90 % to secure admission at MIT.
All the best.

Use the Andhra Pradesh-EAMCET 2018 College predictor at the link provided below:
Use your Andhra Pradesh-EAMCET 2018 rank to see where you can get admission. See the courses, colleges & rounds you may crack. The result is based on admissions data of Andhra Pradesh-EAMCET 2017. Get resources & insights on colleges & courses. https://www.shiksha.com/b-tech/resources/ap-eamcet-college-predictor.

Top executive MBA colleges in India accepting GMAT are mentioned at the link provided below. This ranking is based on the rankings published by Business Today. The mentioned exam cutoffs are for general category students.
Regards.
https://www.shiksha.com/business-management-studies/ranking/top-executive-mba-colleges-in-india-accepting-gmat/18-2-0-0-310.