Pune

The following colleges can meet yours requirements.
1. Dr. D. Y. Patil Institute of Management & Research (DYPIMR), Pimpri, Pune
2. MIT School of Management, Pune
3. Indira Institute of Management, Pune.

Absolutely. MBA is the best option from DY Patil, Pune. A well-known and reputed group of colleges, which offering various under graduate and post graduate academic and professional courses.

SEED Technologies, Mind Scripts, Vision IT Technologies are the software training Institutes in Pune.

Evening/distance/online/part time engineering courses are not valid any more as per the latest supreme court verdict, hence would recommend you to join regular B.Tech course for better career prospects-
http://www.tribuneindia.com/news/nation/no-technical-education-through-correspondence-says-supreme-court/491819.html.

You may get admission in ASMs Institute of Business Management and Research with the above score.

Yes, there will be exam centre in Pune. Details regarding which will be mention on you admit card.

You can see all exam centres here https://www.shiksha.com/architecture-planning/nata-exam

Hello! Yes, if there are business requirements of a particular company in Mumbai, then one can surely get placed there. Generally, the companies have pan-India vacancies to be filled.

It's having a different fee structure for the students as per category and their region. In Maharashtra, out of Maharashtra and abroad students have different fee pattern. Where do you belong to and what is your category? The fee structure is feasible if you are from Maharashtra otherwise it's a little costly.