Colleges in Hyderabad

If you are asking about the Osmania University, Hyderabad, than the eligibility criteria of PG Diploma IN
CHILD PSYCHOLOGY (1 Year) course is given below. Eligibility criteria : Women candidates who have passed Degree in any faculty of this University or any other University recognised as equivalent thereto. Admission criteria : Through an Entrance Test conducted by the University
So from above you are eligible for the asked course.

Yes, you can go for M.A. (History) after your graduation in Bachelor's in commerce. For Master's course the Bachelor's degree with any field from a recognised University.

All the decisions are on hold right now, you will be informed

Yes, without writing any Entrance Test (ET) you can easily get direct admission to MBA.

Yes, you can join directly degree but before that you have to write an eligibility test which is not a competitive test but it is conducted to know that candidate can read, write and understand the course.