B.Tech

Yes, you can get admission for B.Tech in computer science, and you'll get direct admission in second year, mean you'll get lateral entry.

Healthcare management programme at KJ Somaiya is like any other PGDM programme. Score from CAT/XAT/CMAT/GMAT are applicable. Unfortunately no B school accepts GATE score. https://simsr.somaiya.edu/en/programme/ST1735
https://simsr.somaiya.edu/en/admissions/PGDM#profile-v.

Manipal is better than SRM and VIT .

I never heard that any student get any international placement after B.Tech in CSE. But, yes many students go abroad after clearing GRE or GMAT exam for further studies. The highest domestic package offered was around INR. 17 LPA (but not sure for which specialization) and the average domestic package was around INR. 4 LPA - INR. 5 LPA.

What is your category? It is really difficult, if you are from All Indian Category other than Odisha, because the institute has been added to JOSSA from this year, which means the cutoffs will increase exponentially as compared to previous years.
But, don't lose hope and try in as many colleges as possible.

If you have Diploma in engineering, then definitely you can get lateral entry admission for B-Tech.

Yes, at this score there is 60% chances to get admission. If you are not getting admission on your JEE main score you can ask college authority for management quota seats but management seats are totally at the discretion of the college.

See it never depends on the university that offers packages. It depends on you what knowledge you have and how you perform well in the interview. While good universities in which company offers good packages are IIT Bombay, IIIT Hyderabad, IIT Kanpur, IIT Delhi, Bits, SRM and many more just prepare well, have a good knowledge about your field, build good resume and perform well in Interview for good packages.

Dear friend, as per my knowledge and experience, after B.Tech for pursuing MSW, you must have some work experience because without work experience there is no scope for getting admission there. For further details, you can also visit respective university websites. Thank you, have a bright future.