Colleges in Karnataka

You can go to the official site of university and find out that what the eligibility for the same is. You will come to know about that.

Yes, it is available in the above said college. However, you need to apply that separately while talking admission. You have to pass the entrance test in order to get a chance.

Please go through the link:
https://www.shiksha.com/university/pes-university/pessat-mba-exam

Yes, Jain University offers M.Sc. Psychology is Integrated with British Association of Counselling & Psychotherapy, UK. The eligibility criteria is given below.
Eligibility : The minimum qualification required to apply is a bachelors degree in the respective discipline from a recognised university.

Yes. You will become fluent over a period of time.

Yes, you can choose MBA in agriculture after completing graduation in BS Agriculture. But I would recommend you to choose the top B school in India only because it will help you to secure a good job after MBA in agriculture at the top firms.
Hope you got your answer.