Electronics and Communication Engineering

If you want to get a government job then go for civil as it has large scope in future but if you are good in solving circuits and want a job in DRDO then go for ECE.

ECE stands for electronics and communication engineering whereas EEE stands for electrical and electronics engineering. EEE is the parent branch from which many other branches are derived and ECE is one of them. Syllabus and coursework is different for both EEE and ECE. Please refer to the link provided below for detailed comparison between ECE and EEE:
https://www.shiksha.com/b-tech/articles/comparison-between-engineering-branches-ece-and-eee-blogId-8172

Hello A Patel,
Here is the list.
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/colleges/b-tech-in-electronics-communication-engineering-colleges-west-bengal&ved=0ahUKEwj65PugzYDWAhUMrY8KHVuwA9IQFghKMAA&usg=AFQjCNHfzKGn_22iT-m9mSvg2bUfiPjMng

Mechanical engineering is having more scope in the pvt. sector as well as government sector.

Yes, you could get admission but the dates of admission are over.

http://bitsadmission.com/hdmain.aspx
Check this link.

GRE is not required and if you are talking about exchange scheme you have to get in touch with the two universities you are concerned with right now, the one in India where you are currently studying and the one in German y where you wish to go. Best is to get in touch with DAAD too. Check DAAD Delhi website for exchange programmes and norms.