Degree

Off course they can hold a PGDM, even if they hold a distance degree that doesn't cause an issue.
All the best for your bright future.
Work hard and smart to get success. Thankyou.

Yes, you can. All the best for it.

No, there is no possibility, if you discontinue your B.Sc. Now, you have to start from new phase after 3 years.

We have Masters programme in Marketing, Finance, Operations and HR offered here at SIBM-H.

No, they don't offer this course:
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Dear Vora,
Your CGPA qualifies you for a Master's degree, however, the IELTS requirement in most of the top universities is an overall score of 6.5 with no band less than 6, again you need to check the requirement with the university you are applying to or else select the ones which will take you with these scores. The next choice is you retake your IELTS after some coaching and score higher.

Yes, you can enrol yourself for Ph.D on the basis of the provisional certificate which can be obtained from your current college. it will be even better if you can contact your college for the detailed information about this.

No. There won't be any problem. The degree completion date will be required for further form fillings and prof of degree completion.

Hi
Yes, distance learning programme is valid for a government job.