Engineering Entrance Exam

Depends on your category. If you belong to SC or ST category, then you can get good college.

Join IIT coaching and study at home, the school syllabus of class 11th and coaching will take care of IIT JEE syllabus, but you also have to take care that you will have to do some self-study. It does not completely depend on coaching.

You have got good marks, but NIT, Surthkal, Karnataka comes under the top list of NITs.
Not only this, they both are famous for their mechanical branch after NIT, Durgapur and Surat.
So, 139 is not enough as the admission in those NITs starts from 180+ for home quota and 250+ for other state students.

No, it is not possible to get any government college for B.Tech.
You should go for colleges like Gulzar Group of Institutes.
Only for Computer Science and Automation/Robotics.
But, not for civil and EEE.
For civil, you can choose COER and for ECE Chandigarh University.

You should appear for JEE Mains Advanced first.

You can easily get colleges like:-Jaypee- Noida.

Yes, if you have cleared the cutoff score for SC category students, which is given below your score card.

It is very difficult to get into main campus with such rank, but very likely to be selected in any campus.

You will get Electrical in UIET- Punjab University, BIT-Patna, Deoghar, Jaipur campus, chemical in UICET and lower branches in lower NITs.