Vellore

Yes you do. Apply for it.

Coming to the placements at VIT Vellore, it is awesome, and even we got a place in Limca book of records in the latest released records. We get more dream offers that is above six lacs per annum. Mainly for this branch, we'll have an additional benefit of the post graduation degree in the hands, so we had a great chance of placing in good companies. But it creates the problem when all the branches of VIT like Chennai, Bhopal, Amravati are dumped in Vellore for the placements, and you can't say hundred percent placement, but worthy ones will have many opportunities.

Please refer to this link for the syllabus:
http://www.vit.ac.in/files/academics/schools/SMBS/Courses/B.Tech.CivilEngineering.pdf

Just go for the better IIIT's. VIT stands nowhere compared to the better IIITs. Some of the good IIITs are IIIT Hyderabad, IIIT Delhi, IIIT Allahabad, IIIT Bangalore. VIT is just an overrated university. It is a well-known fact for most of the engineering aspirants that if they do not get any college they will get VIT, Vellore by paying donation. VIT is just a money making university.

Average salary
$80,115 per year in the United States
INR 243,041 per year in India. Production engineering is not having that much of scope when compared to other departments. But this won't be a matter when u r passionate about your aim. Good luck!

No option to change branch.

You can get any branch in VIT-Chennai campus.
For Vellore also, you can get most of the branches (maybe except CSE).
Yes, you can also get ECE in Vellore.