Engineering Entrance Exam

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.

There is no attempt limit, but the age limit is present there.

Some of the good colleges under WBJEE are:
Government colleges:
1. Jadavpur University
2. Kalyani Govt Engineering College
Private colleges:
1. Institute of Engineering and Management (IEM)
2. Heritage Institute of Technology
3. Haldia Institute of Technology
4. Techno India
5. NSIT
Colleges are arranged in descending order as per their rank.

If you are choosing your career in mining engineering, NIT, Nagpur is best after ISM,Dhanbad in placement and teaching. Or, if you choose ECE, then go to IIIT, Kancheepuram.

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.