IIM

In view you have got call from IIMs, you stand high probability to clear it this time. Admission to IIMs happens on the basis of multiple parameters, therefore, you must try to do your best in the GDPI. All the best!

For admission in IIMs there are several things which can be considered:
1. Entrance scores
2. Past academics
3. Extra-curricular
4. Social participation
5. GD/PI
After considering your performance in everything they allocate seats.
So, score good percentile in CAT and get yourself a call, rest will come in role after that.

No, for MBA you should be a graduate. Diploma is not a graduation course.

Yes, the CGPA is enough to qualify. You can make to most of the IIMs with this CGPA if you have good scores in CAT/12/10. Focus on maximizing your score in CAT and you are good to go.

It's not compulsory at all. Being a CA gives you advantage in the area of finance as are already aware but it need not hinder you from exploring other areas of management Science. You are completely free to pursue any field and the fact that you are a CA will not be seen negatively. I know many students who pursued Human Resource Management after doing CA and landing great jobs during campus placements. So, the answer is - Study whatever you want, being a CA does not limit you.

Work experience is seen as a positive for any MBA program in general. You are advised to prepare well on your work experience and learnings and use it to your advantage during interviews. JEE in public sector is a good experience. So, be confident when you describe it to interviewers.

Currently, no IIMs offer BBA degree course. IIM, Indore is the only IIM which offers 5-year integrated programme in management with IPM.

Yes, you are eligible. But, you need to crack CAT exam and GD/ PI process to get admission in IIM.
Good luck.

Yes, you have chances to get call from IFMR, NIBM-Pune, WE School, Kirloskar, BIMM. You have a good academic profile which is an advantage. You can prepare for What/PI or GD/PI process as per the college. Prepare well on recent events happening in India and rest of the world. Try to gather news and information on last 6 months happenings.

As good as no for general category. If you are from SC/ST, you can give CAT a shot.