B.Tech

Yes, VIT offers B.Tech in mechatronics.

If you have general or OBC category, then CSE in NIT is not possible.
If you fall under SC and ST category, then you can get CS, but in low college.
For CSE in VIT, you can go, but the fees of VIT is INR 4 lacs to 6 lacs per year + INR 1 lac hostel per year.
For CSE in SRM, your son can get scholarship

You can very well go for MS from any foreign universities,US universities are best for MS. You need to crack GRE and TOFEL(English proficiency test). If you want to pursue M.Tech crack GATE and get into IITs/IISC. A good score in GATE will also open opportunities to get a job offer in PSUs.

Yes, it is possible for a Diploma student to pursue B.Tech.

You may refer to following link for list of top Engineering colleges in India for doing B.Tech:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0
Any graduate is eligible to do 3 years degree course in LLB subject to meeting various universities eligibility criterion.

Both BE in aeronautical engineering and B.Tech in aeronautical engineering are similar degrees with only nomenclature difference.

Yes, SRM offers B.Tech in mechatronics.

It is obvious that you had forced him to do engineering.
But, if he don't want to continue B.Tech, then discuss with your son and let him choose what he wants to do.

Dear Kishore,
It's up to your and skills, of course, you can get good salary packages after doing M.Tech & B.Tech dual degree courses. I would suggest you to choose CSE branch.

Dear Sreeram,
Please understand that there is no difference in PGDM and MBA other than course name. PGDM is equivalent to MBA and syllabus of both are almost same.
Maths is an essential subject in both. There are subjects like Quantitative Techniques , Business Maths / Statistics or etc in both PGDM