Colleges in Surat

Placements are good at this college. You can consider this as an option.

No, you can not take admission in SVNIT without appearing in JEE-Main. All the B.Tech admission in NITs are done on the basis of ranks obtained in JEE-Main. However, you are entitled for 5% reservation quota in your category for admission.

Yes, you have a great chance of getting NIT-Trichy.

What is your interest? If core branches are your preference, then go for mechanical. If you need any private jobs just go for CSE.

You need to check with college officials, if they will allow you to take admission in the 2nd year. You can contact the college and get a better understanding of the same from them.
Link: https://www.aurouniversity.edu.in/contactus.aspx

Hello Anjan,
You have scored quite well. I am sure you will be able to get admission in the college of your desire. However, to be sure, I am attaching a link that will predict college for you. If you are not satisfied, I would suggest you should appear for the exam in April also for improvement in percentile.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You will need to get in touch with the college for detailed information. I think they should offer admission to private students too provided it is government recognized.