Andhra University, Visakhapatnam

Yes, you can. You need to appear for GATE exam for admission in this course.

No, Maths is not required for MBA.

No, you can not pursue M.Sc in human genetics after BDS, details below:
Eligibility
Mandatory Course for M.Sc. in human genetics : B.Sc.
Candidate must have completed B.Sc B.Sc. with any three of the following subjects: Botany, Zoology,
Chemistry, Biochemistry, Genetics, Human Genetics,
Biotechnology, Microbiology and Medical Lab Technology from a recognized University.

The eligibility is Mandatory Courses: B.A., B.Sc.
50% seats will be filled through B.A./B.Sc. course with psychology as one of the paper or specialization and remaining 50% seats to any other degree recognized by Andhra University.

No, you can not pursue from Andhra University.
Details below:
Mandatory Courses : B.A., B.Sc.
50% seats will be filled through B.A./B.Sc. course with psychology as one of
the paper or specialization and remaining 50%seats to any other degree
recognized by Andhra University.
For more details check the link below :
https://www.shiksha.com/humanities-social-sciences/psychology/course/m-a-in-psychology-andhra-university-visakhapatnam-269572

Hi Sandhya, you may follow these links for your syllabus,
http://entrance-exam.net/andhra-university-msc-foods-nutrition-dietetics-entrance-test-2012/
https://www.shiksha.com/university/andhra-university-visakhapatnam/aucet-exam-syllabus
All the best.

Yes, this university offers part-time BFA.