Telangana

Both the brands BITs and IIT are prominent ones. Difference lies in the fees, location near your home, curriculum, placement stats etc. There is difference between the subject content of both the branches. Check this link to know about ECE. http://www.bits-pilani.ac.in/Hyderabad/EEE/Programmes
Make your decision wisely.

Yes, your rank seems very good and you can get admission to Andhra University.
Best of luck.

Could you please tell me about your educational qualification, so that I can guide you better?

Eligibility for M.Tech-
A minimum CPI of 6.0 or 55% of marks in the qualifying degree/Diploma as indicated below:
Note: All regular category candidates (except those having B.Tech/BDes degrees from an IIT with a minimum CPI of 7.0).

Hi,
Of course you can take drop in between Engineering. The fact you will face is you will be considered as DC student. Your degree will be of 5 years duration instead of 4 years. This can put bad impact on your career. I recommend not to take gap. Well, it depends on you what to choose.
Best of luck.

Hi,
12 years of schooling + a 3-year Bachelor's degree in Computer Science or a relevant area* with mathematics as a subject either at the Bachelor's level or at 10+2 (12th class) level from an institution recognized by the government of any of the SAARC countries, with a minimum of 55% marks in aggregate or an equivalent.

Hello there,
Before opting for any college or branch. Firstly, you should check out Shiksha's college predictor. Hence go through the below link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjPs-iFqpTcAhWMRY8KHariB-kQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H