MBA/PGDM

Both are good institutes but are knows for separate specializations. MICA is knows for Media related specializations & IIT madras for Engineering related domains. You need to decide what to pick up keeping in mind your interest areas and long term career aspirations.

This would depend on your interest areas and career aspirations. Since you have explore CA you could pick up finance as your specialization in MBA. In case you are open to career in marketing / sales / HR / operations / SCM then you also have the respective specializations.

Your first need to clear your backlogs and ensure that you secure minimum 50% marks at the graduation level as this is the minimum percentage criteria for admission into MBA based on CAT scores.

This would depend on your interest areas and career aspirations. In case you intend to pursue a career in Teaching / research / academics area then MA is better. However, if you want to move into general management the MBA is better.

I am afraid, one needs to have scored minimum 50% marks at graduation level to get admission into MBA. Since you have only 47% you don't qualify the minimum criteria for admission into MBA irrespective of the score you achieve in CAT.

This would depend a lot on the following factors:
1. Financial stability
2. Long term career plan
3. Interest areas
4. Score in CAT
5. Family responsibility
6. City of stay.

Both are one and the same. Some call it Distance while others call it external MBA. The best part here is that one can continue working & simultaneously learn as well. One needs to do self-study (some institutes, also have the option of some online sessions or some weeks of in-campus learning) & appear for exams.

If you intend to come back to India after doing your Masters in US then it is better that you pursue the said course in India itself as it will give you better exposure to the Indian context of business, moreover you will have the advantage of internship & campus placement as well.

CA is a professional qualification & a person can start his/her independent practice after clearing this course. Whereas PGDM is not so, it is more on the business management side & though being good doesn't carry the same positioning.