Electrical and Electronics Engineering

EEE involves electronics and electrical study while ECE involves the study of electronics and some part of communications.
In core companies, the demand of EEE is more in comparison to ECE. Whereas, ECE students can apply for IT companies as well.
EEE students don't have much scope in IES while ECE students have. ECE can get govt. jobs with high probability than EEE.

For civil engineering, RVCE, PESIT, BMSIT and MSRIT are the best options.
For electrical, PESIT and MSRIT are the best options.

Please refer to the link provided below for details on fee structures of B.Sc. in EEE from IIT Bombay. You should be able to download their brochure via which you can understand their fee structures for course in B.Sc.
Link: https://www.shiksha.com/college/indian-institute-of-technology-bombay-iit-powai-mumbai-28130

Eligibility criteria for admission in Diploma in Electrical & Electronics Engineering is 10th pass. You are eligible to seek admission in Diploma in Electrical & Electronics Engineering in any Polytechnic.

Firstly, clear all your concepts from the subjects in B.Tech EEE and stay focused. Go for Made easy (GATE coaching institute) take the test series or classes on weekend or online lectures that would be suitable for you. The questions in GATE are based on the logic which can be cracked by through in-depth study.
Good luck.

You can take admission in BITS-Pilani, UPES and some NITs.

If you want to do government jobs then you should take the civil branch, otherwise, you should take EEE branch. In civil engineering, you can also take a private job but government jobs will be better. First, you should decide that in which stream you have interest and then take any decision.