CBSE

For taking admission in NIT one should have 75% in class 12th. You can try for your state government engineering colleges. Hope this helps. All the best.

Please mention your category.

You should first clear your maths and pass in it. Only after that you will be eligible for any UG course. But you can do Diploma on 10th basis.

Yes, 280 marks is a decent score. Use Shiksha College Predictor to know the college you can get.

Yes you are. You might even get your preferred course.

280 is a decent score. State your AIR or use Shiksha college predictor service.

Rarely, there is a chance for you to get into such a prestigious college with that percentile.
But don't worry. Try other colleges. You will surely make your life better, there too.

Your brother can opt for Improvement in the subjects he recieved less marks. For that refer to the CBSE Website at https://www.cbse.nic.in
Also refer to https://www.toppr.com/bytes/cbse-improvement-examination/for more information. Other choices your brother has are that he can pursue a UG course at local college and prepare for a UPSC Exam simultaneously.

Honestly, no one leaves CSE branch seat. If there's any seat left, students from other branches will take it. As you haven't given JEE, there's a very little chance to get admission in a branch of your own choice.
But yes, last year, at the end, admission to Thapar was open to all. You could get a seat in the branches available at that time.
Usually, Electrical, Chemical, Mechanical, Civil have some seats left.
Rest, visit www.thapar.edu for more information.

Yes, definitely, you will got an engineering in any state, as per your JEE marks.