M.A

Yes, you can do it because this field has a lot of scope. If one chooses to work for himself, for their passion, he/she can go for-
English teacher
Author
Blogger
Research
Scopes in different companies-
Advertising
Editor for some reputed publishers
Book translator
Writing subtitle for movies
Advertising
Scriptwriter
English tele-caller
KPO firms
Journalism and many more
If one wishes to study further, they may opt for-
Master of Journalism
MA Communication
Master of Communication studies
Master of Journalism and Mass Communication
Master of Mass communication
Post graduate Diploma in various fields
Communication Management
Film Editing and Direction
International Relations
Law
Tourism Administration
Visual Communication

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.