VIT Vellore

You have a good score in GRE and IELTS keeping that in mind you can do MS from foreign in Data Analytics as you are good in Python and R. You can easily get a scholarship in foreign.

This year, VIT seems to not accept UCEED ranks. Check VIT's official website www.vit.ac.in for more details.

No. VIT doesn't have a course as of now (2019) in BBA in Hospital Management.

To pursue CSE at VIT, you should appear for their entrance exam. Since you mentioned that you belong to a poor family, then getting very good rank in VITEEE is of utmost importance, as they provide some scholarship to the meritorious students based on performance. Good luck. Hope it helps.

RVCE: 1
VIT: 2
DAIICT: 3.
RV College of Engineering focuses on each and every student of every branch and that's the reason they have limited number of seats in each branches. Bangalore is the IT capital so most of the students prefer computer Science as the 1st priority, but seeing There teaching methodology you can take any branch as per your interest and you will be in safe hands. R. V. College of Engineering was set up in the year 1963 spread over 51.4 acres on the banks of the Vrishabhavati River in Bangalore. The autonomous institution is affiliated to Visvesvarya Technological University and is approved by NBA, AICTE, New Delhi.

In order to get into VIT you need to be in top 1 Lakh. If you aren't in top 1 lakh in VITEEE you can't get admission in B.Tech programs.

You can't switch campus while pursuing a course. You can change the campus at the time of counselling or before one month of your first instructional day.

For doing M.Tech in Software Engineering integrated, you need not write VITEEE. You just have to apply with your class 12th marks. Get an application form and attach your class 12th marks to it, and just submit it, both online and offline mode are available.

Both the institutes are quite good and have their acclaimed merits but if given a choice to choose definitely BITS, Pilani is a better option.
All the best!