Mechanical Engineering

The eligibility criteria for PG Diploma is to pass in graduation with at least 50% marks for general category.
If your Mechanical Engineering is a Graduation degree, then you are eligible.

Will you be able to do Part Time Engineering or Evening classes? Those are options you have in engineering field. I would have suggested AMIE, but it is not recognized by AICTE. IGNOU on the other hand provides B.Tech in Civil Engineering only, so that is not in equation. There are many colleges in Delhi that will give admission to working professionals.

You are eligible to pursue M.Sc in Physics after B.Tech in Mechanical Engineering.

Yes, you surely can. AICTE has given this task to the institutes to decide the eligibility for admission in any course. So, if you can convince the administration that your course is similar to Mechanical and that you would be able to study B.Tech without any problem. Then they may give admission.

That is a very nice career choice you have made. I hope you are pursuing B.Tech in Aeronautical Engineering. This is a great course and will surely open opportunities for you in aviation sector. The demand for such courses has increased in past years due to rapid development in the Aviation Industry. The demand for aeronautical engineers has also increased no doubt. So it would be a very good experience for you. All the best for your future.

Yes, you can apply to get admission here. PG Diploma is pursued after completing graduation which you have done with 69% marks. You are eligible for admission here. You graduation branch doesn't matter for this course.

IIT Kharagpur in my opinion is very good for Mechanical Engineering. Swami Parmanad Group of Institution is below average institute in my opinion. You can read reviews about it here. https://www.shiksha.com/college/swami-parmanand-college-of-engineering-and-technology-mohali-23212.

Study well fundamentals

It does not depend on the branch. Rather, it depends on the set of skills which the individual possess. One BM branch individual can even be ahead of CSE individual so opt for the branch you like. Good luck.