Babu Banarasi Das National Institute of Technology and Management

Yes, you can definitely get BBD, but try for other good colleges through counselling or direct admission.

The counseling done in colleges are mainly about your interests etc. Its not very tough. You do not need to prepare for this. just be confident in answering. Most colleges use counseling to promote admissions in their respective college. But top colleges where the seats are limited there the confidence of the student matters a lot.

https://www.shiksha.com/college/babu-banarasi-das-national-institute-of-technology-and-management-Lucknow-28153/admission
In this link, you will find all the information related to admission procedure along with the eligibility, important dates, etc.

Yes, you can get admission in B.Tech for Mechanical Engineering Branch, but you will not get Babu Banarasi Das National Institute of Technology and Management College with 61% in Boards and 51% in PCM you have to try for other colleges.

Yes, you are eligible.

If you are scoring a rank in between 15 thousand to 20 thousand, you will be eligible.
In terms of numbers, it may be 200 to 250 marks.

You have sufficient grades in your M.Com, you are eligible for pursuing MBA.

The average salary offered is Rs. 4.6 LPA and the highest salary offered is Rs. 6.5 LPA. Therefore, I would suggest you to think and then choose.