Rajasthan

Yes, you can get it, if you have clear the first year with 60%.

Yes, for sure there are & there will be vacancies for agriculture engineers in Rajasthan.

Graduates with MBA in finance and banking have good scope and job opportunities in both public sector or private banks or financial institutes. If you do MBA from a good college in Jaipur then you have good chances of getting a job.

Don't opt for a branch based on the college. In fact, go for the branch in which you have interest, and are most passionate about. You should analyze the scope and future growth prospects before taking admission in a college to pursue the course of your choice.
You can also opt for psychometric test comprising of aptitude, personality, and career interest.

Dear,
There are institutes in Jaipur which charges the fee from 5 lacs to 1 lacs. So, prefer accordingly based on your economic conditions.
All the best.

If you are asking for correspondence, then you can go for IGNOU. You can also do it with your job. If you want to do regular BA, then ICG, Kanoria, Raj University or Amity are few.

Can I know about your graduation percentage, CAT or GMAT score?

Dear Abhijeet,
Out of these two, your first preference should be Amity, Jaipur and second option should be VIT, Vellore.
All the best.