Hindi

It is a very good degree. You can pursue PG in Hindi literature and post that you can go for Mphil and PhD programme. This will help you get a good start in Govt. college.

For PGT job in schools, you need at least B.Ed qualification. With the only degree, you will not be eligible for any teaching job. Most of the top schools will ask for B.Ed qualification which is the minimum requirement for teaching jobs these days.
Also, if you want government teaching job then you have to qualify TET which is also the for only B.Ed pass candidates.

Yes, you surely can.
A language subject has necessarily to be included in the best of 4, so, you can include Hindi core.

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The first and basic qualification required for a Ph.D. course is that
you must have completed your Masters degree course.
To apply for Ph.D. you can either directly apply to the professors of
different universities sending them your resume , Statement of purpose
and your research papers. Or you can appear for UGC-NET examination
and then sending your NET scores to the professors under whom you want
to undergo your Ph.D. course.

You had not mentioned your specialisation in degree. Yes, we have the option to choose between languages like Hindi, Sanskrit, Urdu, French, etc. As usual, 2 years of degree you will continue language subjects.but in final year you can not. You can do B.Ed in Hindi methodology and the MA from reputed colleges then it is helful in the career.

Hi Raghuvendra,
There is no language barrier in NSB. We have students from 28 different states and from different mediums of educational backgrounds. What is important is how you clear the tests and interviews by the college along with your marks in your previous qualifications. If the college feels you are really the best fit, then you will definitely be selected even though you are from a Hindi medium.
Hope this answers your question.

Hi Shareef,
Kindly check the same, here:
http://dbhpskerala.org/courses.htm
All the best.