B.A Scope

After BA in any discipline, you can go for Masters i.e MA in your honours subject or even in the optional subject you have chosen. Secondly, you can go for MBA which is one of the most demanding courses. If you are interested in matters of law then you can go for a 3 years LLB and continue your career as a lawyer. There are lot other courses provided by different colleges and universities which can give you a better perspective for your future.
If you are considering for a job after graduation then there are also many opportunities. Most of the government and centralized banks jobs have graduation as their eligibility criteria. So, you can apply there. Private jobs with the only graduation will not fetch you a good salary. For a private job for a decent amount of salary, you should have a postgraduate degree.

Yes, you can do MA after completing BA. You only need Bachelor's degree in arts stream for taking admission in MA Sanskrit.
Academic options:
Upon successful completion of the course, postgraduates interested in further studies in the discipline may go for pursuing MA in Sanskrit literature, B.Ed or PhD in Sanskrit or Masters in mass communication and journalism with specialisation in Sanskrit Patrakarita.Other options include pursuing Postgraduate Diploma in Functional Sanskrit and Translation, or Post-Graduate Diploma in Sanskrit Journalism. Rashtriya Sanskrit Sansthan also offers such postgraduates the option of taking vocational training in Sanskrit short-hand and typing and cataloguing manuscripts.