Colleges in Hyderabad

Refer this link: http://www.osmania.ac.in/sciencecollege/forsci.html.

Yes Pavithra, you are eligible for the course. PGDM in ABM is just like any other MBA/PGDM program. We take in students of any stream from any college/university.
For this year, admissions are over. If you want to try for next year, then start preparing for CAT. Give the exam in the month of November. Fill MANAGE application form that will be available till December 31, 2019. Appear for essay & GD/PI in the month of April 2020, if you are successful, then you will be the part of 24th batch of MANAGE, PGDM-ABM Program.
Keep striving for excellence!
For more details visit: manageites.org

Yes, you can join. But, this is totally at the discretion of the college officials. You need to have valid reason for such a long gap in studies.

No, there is no such age limit mentioned on the official website.

You need to have a minimum of 60% to be eligible.

In St. Francis College for Women, Hyderabad B.Sc fees is around Rs 30,000.

Hello Yakub,
Recently, just a few weeks back, UGC has announced that all distance education courses in professional subjects are banned. Diploma in agricultural engineering is also a professional course and I would not like to advise you to go for Diploma via distance education mode, even if some institutions are offering this.
Best wishes to you.