CAT

You can consider the below mentioned colleges:
1. MANAGE - Hyderabad.
2. NIBM - Pune.
3. XIME – Bangalore.
4. Great Lakes.
5. IMI – Bhubaneswar and Kolkata.

Yes, you may get a call.Conversion depends upon your performance in GD PI.

Yes, you have a good chances of getting an interview call as there is no section wise cutoff for MBA at BITS Pilani.

Chances of getting a call depends on the cut-off percentile and has no relation with years of experience.
Years of experience is considered after shortlist during GD/PI.
There is no fixed cut-off. Last year, cut-off for CAT- 86 percentile , XAT - 78 percentile and CMAT - 96 percentile. ATMA scores are not accepted for PGDM.
For more information refer brochure:
https://www.somaiya.edu/media/pdf/PGDM_Admissions_Brochure_2017-19.pdf
Online Application Form: http://simsr.somaiya.edu/simsr/adm/pgdm17/onlineform/login.aspx
Placement Report: https://www.somaiya.edu/media/pdf/Placement_Report_2015-16.pdf

S P Jain requires a higher percentile and you need to have a very good profile to get selected. Score above 85 percentile minimum.

TIME is well known along with IMS, Career Launcher, CPLC which are competitive and have good results with list of CAT toppers. You can choose any of above according to your convenience.

No, you will not get a call from the IIM to which you have not applied.

You can apply for:
1. ITM – Mumbai.
2. Balaji Institutes – Pune.
3. MIT – Pune.
4. Flame University – Pune.
5. IPE – Hyderabad.
6. ASB - Coimbatore.

Yes, it is a good score to apply. You can get into some good B-schools like IFMR and Welingkar. Both have CAT cut off around 80-85 percentile.