Surat

You can join IIT Surat. Scope wise, you would get the opportunity to sit in placement with SVNIT guys because it will not be established till then and the best part is that you can join this institute at low ranks!
You can join it through counseling but all depend on you.

No, but yes, it's improving day per day.

CSE in NIT-Bhopal is better than chemical engineering in Surat, no matter that NIT-Surat is far better than NIT-Bhopal, but taking core branch is highly beneficial than taking a non-core branch.

CS at NIT PATNA.

Kindly follow the below link to follow the fees for M.Sc physics in South Gujarat University, Surat
https://www.google.co.in/amp/s/www.shiksha.com/science/course/amp/m-sc-physics-veer-narmad-south-gujarat-university-surat-171746

JEE Mains 2018 college predictor:
Use your JEE Mains 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges and rounds you may crack.
The result is based on the admission data of JEE Mains 2017.https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

B.Tech in automobile engineering colleges in Surat:
P Savani University | Surat
UKA Tarsadia University (UTU) | Surat
For more details of colleges visit the given link:
https://www.shiksha.com/b-tech/colleges/b-tech-in-automobile-engineering-colleges-Surat

As per placement record both colleges have a good package. NIT, Surat has an average of 8 lack per annum. While Kurukshetra has an average of 5 LPA. In terms of academics and whether both are good. For a North Indian guy Kurukshetra will be better option.

Please refer to the link provided below for a detailed comparison between NIT-Surat and NIT-Nagpur for a course in CSE. You should be able to decide which college you prefer after comparing the features of each of these colleges. https://www.shiksha.com/resources/college-comparison-182107-61703.