Exam

You can't get government colleges as your chances are very very low. You can get a good private engineering college in your city/town or state. It depends on your JEE marks and your category as well. Fill the JOSSA admission form properly. Do the research on engineering colleges in your City/ State

Yes, that's a good score. You have a fair chance of admission. Keep hope and apply.

Yes, you can go for CPT December as you have passed 12th. Don't worry about maths as maths questions are up to 10th only and you may join coaching so that you get better idea of papers.
Best of luck.

For getting admission in good colleges, you must have to give entrance exam like CAT, CMAT, etc. If a college gives you admission without any entrance exam, don't go there.

I think you can get top NITs with this rank.

Sorry to say, but it's going to be very difficult for you to get admission into a good B-School as they need minimum of 50% marks in graduation. However, there are certain B-schools like FMS and XLRI which do not give too much importance to the academic scores. So, you have some chances there. Never

It's the entrance exam for getting admission in Manipal Institute of Technology.

It depends upon your advanced result. As now a days, NITs considers JEE Advanced.