Engineering

No, there are no chances to get government seat in NHCE Bangalore for BE electrical and electronics
Good luck.

Yes, your rank is good enough to get lateral entry here.
Good luck

You can use college predictor to know about this:
https://www.shiksha.com/college-predictor
Good luck.
If you want to leave engineering, then you can leave it. But, at this time you might get admission in some other course. So, you will gap of one year. And, if you pursue CSE with interest, then you can have good opportunities ahead. Good luck.

Yes, you can get admission here for your Master's degree. Good luck.

According to my knowledge, you should choose IGEC for better opportunities and facilities.
Good luck.

You can take ECE, because you will get use of mathematics. So, you can perform well. Good luck.

I don't know the exactly amount, but you will have to pay lesser than this.
Good luck.

You can apply for admission. You may get admission there, because seats are available. Good luck.

You can use college predictor to know about this:
https://www.shiksha.com/college-predictor
Good luck.