IIM Ahmedabad - Indian Institute of Management

Graduation then clear civil service exam

I don't think you would. You would not clear BE cutoff, which is usually 60%. But these criteria change every year and if you do really well in CAT, you might get calls from few IIMs that don't give much weightage to BE marks.

The only solution for this is practice. I would encourage you to practice more and more. If you can, form a group of three to four friends and make it a point to converse in English always. At the same time listen to audio books of novels or whatever you are interested in. You should also try to write one essay daily, it will help you in restructuring your thoughts in English. And lastly, get a subscription of good English daily newspaper or magazine and read it loud daily for at least 30 minutes. In short, more you practice, better you will be.

You should aim for JBIMS Mumbai SIMSREE Mumbai FMS Delhi these are top colleges with very low fees and excellent placements

To be very frank it depends on the batch. Also There is very little wait list movement at IIMA. That said I guess wait list 8 should get converted.

No you can not. You need to appear for the entrance examination.

If you have cleared all the backlogs and have received the degree in time, you are eligible to appear CAT given you fulfill minimum percentage requirement. Here is the details about cutoff requirements.
http://www.iimahd.ernet.in/users/admission/files/Admission Procedure_2016_2018_August_10.pdf

If you have cleared all the backlogs and have received the degree in time, you are eligible to appear CAT given you fulfill minimum percentage requirement. Here is the details about cutoff requirements.
http://tinyurl.com/hjg3qsm

And that is why you probably did not receive interview call from IIMs. Also I don't think that you will receive interview calls from IIMs with 83 percentile. I would suggest you should prepare well next time.