Applied Psychology Eligibility

Yes, you can study M.A. Psychology after BBA. As the demand for psychological counselling is increasing day by day, so M.A. Psychology's scope and job opportunities would be a good option.

B.Sc courses that guarantee good jobs after graduation-#1 B.Sc Agriculture.
#2 B.Sc Horticulture.#3 BVSC (Veterinary Science)#4 B.Sc. Forestry.
#5 B.Sc. Biotechnology.
#6 B.F.Sc. (Fisheries Science)#7 B.Sc. Nursing (update)#8 B.Sc. Nautical Science (update).

Yes, one can definitely do MBA after doing Bachelors in applied psychology. Amity University, Lucknow could be a viable choice for both.

Yes, you can apply for Masters in psychology. They require a graduate degree. Many of my known were doing Bachelor's in other field and did their MA psychology. You can try for clinical psychology also. One of my friends got recruited in AIIMS as psychiatrist after doing MA in clinical psychology.
Go for it.
Regards

No one can guarantee you placement in any college. It is always about probability, your hard work, your choice of work, etc.