Mysore

Obviously Computer Science is a better choice. And it also have good career prospective.

Not better than RVCE & BMSCE. NIE is better than all other colleges you'll find in Karnataka

Deepika, I suggest you look for a job which has some kind of foreign connections. That will be better for you rather than searching for a short-term course. If you get a job in a company which has some foreign connection (say if it is a MNC, or if it is an export-import comPany or an Export house or a 100% EOU) you can then plan your certificate course to make you prominent and more successful in that company. So search for such a job not for a short-term course after MBA. That is my suggesstion.

Yes, you can apply for a management seat. you'll have to pay more for the branch. depending on its demand.

There are various colleges in karnataka for CSE.
1. MANIPAL INSTITUTE OF TECHNOLOGY
2. R.V COLLEGE OF ENGINEERING
3. M S RAMAIYAH
4. VTU
5. PES UNIVERSITY.
Best of luck.