MBA/PGDM

For this, you need to talk to the admission cell of your college.

You can refer the below link for colleges offering MBA in marketing with specialisation in digital marketing.
https://www.shiksha.com/mba/colleges/mba-colleges-india?uaf[]=location&uaf[]=exam&uaf[]=specialization&ts=8174535&rf=filters&sp[]=141&ed[]=et_20

Deviprasad Goenka Management College of Media Studies, Malad West, Mumbai
Digital Marketing Training Institute, Chembur, Mumbai
You can also refer the below link: https://www.shiksha.com/mba/colleges/mba-colleges-india?uaf[]=specialization&ts=8174411&rf=filters&sp[]=141&ed[]=et_20

MBA has specialisation and not categories. MBA institutes have category such as tier 0 (ISB, IIMs XLRI) then tier 1 such as newer IIMs, NMIMS, JBIMS, FMS Delhi IIFT etc) then tier 2 as well as tier 3 MBA institutes.
As far as specialisation concern traditionally and most popular there are around 7 to 8 specialisation and tom dick harry kind of organisation come with their own specialisation. It purely depends on your interest level which specialisation you want to choose. You may choose IT and system or you may choose operation considering your background.

No, polytechnic is a 3 years diploma which is equivalent to a 10+2 qualification and not a degree. He has to complete his graduation with minimum 50 percent marks first in order to be eligible for CAT as well as other entrance examination for admission to an MBA program.

You can prefer SBIIMS as it is listed and by my experience, it is one of the amazing institutes for MBA and as your concern is about operations management, then I would love to inform you that we have amazing faculty members and mentors for each of this specialisation.

IIM-Nagpur is new and will take time to gain reputation and placement . It is better to go for IIT-Delhi.