Guru Gobind Singh Indraprastha University

Hello Vibhor!
Choose SRM University main campus, Chennai. It offers better education and it is known for its placements. But don't go for other campuses of SRM University.

No, but you can appear in CET.

Well, see our highest domestic was 14 lakhs INR and international was 18 lakhs INR. I really don't have much information about the other college, hence would like to not comment on that.

Please visit this link:
http://blog.entranceexamcds.com/entrance-exams/engineering/ipu-cet-guru-gobind-singh-indraprastha-university-common-entrance-test-2017
There, you can know more about GGSIPU eligibility, application form, selection process, etc.

Yes, you can get admission in IPU, and if you want you can also apply for management quota in IPU.

Chances are high. But, I think you need to check the last year counseling ranks and colleges accordingly. You can get the admission easily, as if you fill the choice form according to your rank and colleges selection. So, please go through last year results. It may help you in selecting the colleges

There are almost no core companies in any of the IPU colleges for EEE.
Undoubtedly, MAIT is one of the best colleges in IPU, but not good enough to take any branch just to be in the college.
My advice is to consider branch over college.