Goa

Hi, With this score it will be difficult for you to get admission in any MBA college. You need to score atleast 70 percentile to get admission.
https://www.shiksha.com/mba/colleges/mba-colleges-india?uaf[]=location&ts=26719621&rf=filters&ct[]=89&st[]=108&ed[]=et_20.

Institute of Hotel Management, Catering Technology and Applied Nutrition, Goa
Public/Government | Established 1968
Affiliated to Indira Gandhi National Open University
Ranked 11 for Hotel Management by The Week 2017
Please download the college brochure for expected cutoffs required to secure admission in this particular institute.
https://www.shiksha.com/college/institute-of-hotel-management-catering-technology-and-applied-nutrition-Goa-Goa-other-919

Goa Institute of Management (GIM) accepts XAT GMAT and CMAT apart from CAT scores. A score around 85-90 percentile in CAT is good enough to get a call from GIM. Some colleges accepting NMAT scores are L.M.Thapar, MISB Bocconi, Woxsen, IBS, Shiv Nadar University, UPES College of Business Management and Economic Studies, Alliance School Of Business, XIM-Bhubaneshwar, apart from Narsee Monjee colleges.

This is very specific questions to answer. It is better you focus on one thing, either internship or job, none of the institute focus on both the things.

Yes, you will get good colleges in Pune, Kolkata, Goa, Chennai and Bangalore. But, the chances of getting more would be in Kolkata and Pune, because with this score you can only get colleges in Pune and in Kolkata.

Yes, you will get placement if you go for WeSchool or as well as in GIM. Both are one of the best B school.

Birla Institute of Technology and Science, Goa is the only electronics engineering college in Goa. For more details check the link below:
https://www.shiksha.com/college/birla-institute-of-technology-and-science-goa-goa-other-23311

Goa College of Hospitality and Culinary Education offers programme for Bachelor's degree in culinary arts.