Diploma

You can pursue the same from IIMM. This course will help you to make a good career in the store management field.
For better career, you should pursue GDMM, PGDMM or MBA. To get a managerial position, you need to opt for Master's degree.

Yes, you can. As per me, your decision is a waste of time and money. You have done your Diploma in the same field, so try and make your career in the field in which you completed your graduation.

AMIE doesn't consider a distance Diploma as a criterion to offer admission, but if you have done it as a regular student then you can pursue the same.

Dear Siddarth,
If you intend to pursue your higher education in the same field, you need to check out with the university chosen by you as to which level they can admit you after they check the subjects taken by you in your Diploma. You also need to score good marks in IELTS exam.

Diploma in engineering is not equivalent to graduation. For post-graduation Diploma, one needs to have a degree in engineering. I am sorry to inform you that you are not eligible for this course.