BBA

It is a very good college and their integrated MBA programmes have a lot of value in the market. The placements are excellent and comparable to new IIMs.

You need atleast 60% marks in 12th to get into Christ.

Nothing but the HR. This is the best in class specialisation for girls. If you take a survey, more than 70% of the MBA girls candidates will choose HR as an option. This is because you can sync both your family life and corporate life together.

IIM, Indore would be best for integrated courses.

BBA+MBA is a good option,
Admission procedure for the 5-year Integrated Programme in Management (IPM) at IIM, Indore is you need to clear IPM Aptitude Test (AT). A computer based test for the course conducted in May. The candidates are selected on the basis of overall performance in AT and personal interview.
Eligibility criteria: Minimum 60% in standard 10th/SSC and Standard 12th/HSC or equivalent examinations, maximum 20 years of age as on July 31, 2016.

I'm not sure if MBA colleges offer PhD. I guess you are looking for PGD (Post Graduate Diploma) in Business Management. The average salary for the top B-Schools is in the range of 12 lakh to 19 lakh. For colleges which fall in the second grade, the average salary ranges from 8 lakh to 12 lakh. For other colleges, you might get an average salary of about 5 lakh to 8 lakh.

B.Tech students have advantage of strong quantitative aptitude, so they are good with numbers. Despite of choosing other courses, if your quant is strong, one can score better and hold good positions.

Digital marketing and data analytics are good to choose from as they have good scope.

MBA in IT will not lead your son to software development, but it will lead him to software marketing and other infrastructural maintenance.
All the best.