After Post graduation can we do Graduation again then will the degree be valid.

1. In your BA your subjects are Mathematics, Economics and Hindi are your main subjects. English is also one of the main subjects. Once you passed your BA, you can go for B. Ed by selecting any two subjects from the above four subjects.
2. The Subjects you have studied for 2 years out of 3 years can be taken as permanent subjects. If you want you can opt for B.Ed in the other subjects you have studied in BA.
3. You have to apply for B.Ed when the advertisement comes. There are some universities offering B.Ed through a correspondence course. You can apply for B.Ed in such universities. IGNOU is also offering B.Ed through open university. Once the notification comes you have to apply and appear for the written test and based on your performance you can be given a seat.
4. WIth diploma in education you are not eligible for the promotion. But once you complete your B.Ed, you will get the eligibility for promotion.
5. There is no necessity for appearing for BA again. With the present degree itself, you can do B.Ed. Again doing BA means another 3 years you have to spend. Take Hindi as a subject in B.Ed and go ahead.
6. IGNOU is the best university for doing B.Ed. Anna University is also giving B.Ed through correspondence education.

Yes it is valid even before fifty years. Doing graduation in one faculty, then post graduation in the same faculty and later doing graduation in another faculty is admissible and the same is based on the interest of the pursuing person only. During the academic period 1973-77 itself, our Economics Lecturer one Mr. Narasimhan did M.A.,B.Com,
Our Commerce HOD Mr.C.S.Krishna, hold his qualification as M.A., M.Com., L.Lb during that period.

In relation to your queries, here are my point wise explanations and hope these points will help you in taking appropriate steps -
1) While observing your papers taken in different years while persuing your B.A. It is observed that Mathematics, Economics and Hindi should be treated as your main papers. English, too, would fit in the main one. In order to continue B.Ed. after graduation, you need to select at least two papers covered in your graduation stage.
2) The permanent subjects for your three degree would include those subjects which were opted in two consecutive years. While choosing the subjects for B.Ed, you can take any two papers covered while undergoing the graduation course.
3) Once the advertisement for admission to B.Ed appears in some leading papers, you can take up initiative for admission subject to condition that you fulfil the eligibility criteria with respect to the marks as set by the admission committee apart from the written test if any introduced by the committee. The aspirants are finally selected on the basis of their performance before the interview board.
You can persue B.Ed from IGNOU provided you clear both written and oral test as prescribed by the admission committee.
4) Diploma in Education cannot yield you promotion and for this you have to complete your B.Ed.
5) There is no requirement of further persuasion of B.A course since your present degree alone would serve your purpose for persuing your B.Ed course. Take Hindi as one of papers while doing B.Ed.
6) IGNOU is the best in terms of their quality inputs provided to aspirants apart from their doubt removal session conducted by the subject experts. Karnataka Open University and Anna University are also popular for their quality teaching. Decide the university as per your convenience.

You are already working as a primary teacher. If you want promotion then as per the KVS requirement B. Ed. would be an essential qualification which you have to acquire. Now let us go through your query point wise -

1. Your main subjects in BA are Economics and Mathematics. You have also studied English and Hindi for 2 years. So these 4 subjects are available to you for making a choice when you opt subjects in B.Ed.

2. As you have done MA in Hindi, it makes sense to take Hindi as one of the subjects in B.Ed.

3. As already mentioned above, B.Ed. is an essential qualification for TGT and PGT in KVS schools. So one has to acquire that. Another thing is KVS inducts direct teachers in its TGT and PGT categories and a few positions are reserved for the departmental candidates also. It is natural that there would be competition for these departmental positions and those who are having the eligibility only will get the promotion in addition to the annual performance issues and other such credentials.

4. You have already a good choice of subjects in hand and I do not see any need of doing BA again with some other combination of subjects.

5. There are many good open universities for B.Ed. and some of them including IGNOU are as follows -
i) Indira Gandhi National Open University (IGNOU), New Delhi.
ii) Annamalai University – School of Distance Education, Chidambaram.
iii) Bangalore University – School of Distance Education, Bangalore.
iv) Himachal Pradesh University – International Centre for Distance Education & Open Learning, Shimla.
v) Panjab University – USOL (University School of Open Learning), Chandigarh.
vi) Sri Venkateswara University – Directorate of Distance Education, Tirupati.