CBSE 10th

Hi,
You are eligible for BPSC. For more information you just click on that link. https://www.shiksha.com/nursing/colleges/pb-b-sc-colleges-india?rf=searchWidget

Yes, you can go for mechanical engineering after 10th, but only in the field of Diploma & ITI in ME.
After that, you can pursue in B.Tech in ME by lateral entry scheme direct admission in the 2nd year of B.Tech graduation.

Yes, you are eligible to apply in Great Lakes.

Yes, you can get admission in this college, but you have to apply for the polytechnic entrance exam with a good score.

Yes you have a high chance of getting into an IIM with that rank.

Firstly, you have to complete your class 12th from a recognised board.

Your GMAT score is fine, means (Good > 630 > Average). Your college, class 10th and 12th score is also fine. Now, depending on your non-academic profile and job experience, I would suggest you to apply for some other good college as well. IMT (it is not specifically mentioned) doesn't accept GMAT bu

Yes dear you can get admission. All the best.