Ph.D

I have shared below the complete details about your query.
http://csirhrdg.res.in/jrfsrfra2.htm

Please refer to attached link for list of university which allows CA to pursue PhD:
http://resource.cdn.icai.org/26417bos15829.pdf

Yes why not. However, you must have completed PG.

Delhi University, Bombay University and ISB Hyderabad are one of the best for PhD in India.

MBA and PhD in the same college is a rare possibility. Please do not constrict yourself to a single city. MBA is all about exposure and practical learning, it's always preferable to move out to different state or city. You have AMmity University in Delhi which provides such course and also ISB Hyderabad.

Hello,
Thanks for Asking. Yes, you can go for M.Sc. or Ph.D. or dual course after completing your B.E. You can pursue M.Sc. from IIT's or IISC. To get admission in IITs, you have to clear its Entrance Exam - IIT JAM.
Click here to Know more about IIT JAM Physics - https://www.youtube.com/watch?v=4SBAhhto08M
I hope it will help you.
Best of Luck.

Edit
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You may face challenges in getting admission in Ph.D abroad because with MCA degree by distance learning you may have difficulty is showing consistent academic performance. You are advised to try seeking admission in German universities. You may also not face similar challenges in India.

Hello,
Thanks for asking.
If you want to go for Assistant Professor only or Junior Research Fellowship, you have to clear CBSE UGC NET exam.
This exam is to determine the eligibility for junior research fellowship and assistant professor.
If you have any doubt about UGC NET Exam, checkout-
http://entranceexaminformation.blogspot.com/2016/05/cbse-ugc-net-exam-aspirants-queries-5.html
I hope it will help you.
Best of Luck.