Exam

It depends on you as if you are satisfied with the college and branch, then you can freeze the option and pay rupees 5000.

You are not eligible for admission into any college through JOSAA counselling.
There is no chance of getting any thing at verification also.

NIT-Trichy, NIT-Warangal, NIT-Calicut, MNIT-Allahabad, NIT-Durgapur.

No, I don’t think so. Go for cutoffs in previous years, you will get a very fair idea.

Probably, in internal sliding or in last round. But, chances are very low. Although in 2015, last candidate was around 9500 (after every round that did happen including internal sliding), but can't be sure for this year.

The only problem you may face is relieving letter from college. As you are already enrolled in a private college and also with university so they might demand full four year fees from you.

To get admission on any IIT's you have to good rank on JEE(ADVANCE) or for NIT's you have to be meritorious on JEE (mains). then according to category reservation and cuttoff can get admission.