Query about legal degree validation

Already you did your MA English, B.Ed and B.Sc. Please know that
1. You can do now BA. One person can do two or even more graduations. There is no issue with that.
2. After completing BA now, you can apply with a new BA certificate and an old B Ed certificate without any problem. But please be noted that the BA degree now you are getting should be from a UGC recognised university.
3. What is the percentage you obtained in your MA? If the marks are above 50% even you can go for a lecturer post.
4. Now it will take 3 years for you to complete your BA. Instead of that, join some private college as a lecturer and then register for your PhD degree and start working for a PhD. You can complete your PhD also in three years and your future will be good with higher chances for a good career.

All in all you have done two Bachelors Degree (B.Sc (regular) and B.Ed Science and English (distance)) and two Master Degree (M.A English (private) and M.Sc (distance) 2019)). And, you would like to again pursue B.A in English (private) confusing what would happen to already completed and qualified B.Ed.

You have got a better guidance and reply above.

Instead of going further for B.A in English (to improve or other reason), you can try it for PhD in the same as you have already done M.A English.

In general, some don't have even one Bachelor Degree or Master one. You got it enough and appreciate it. You can plan to study further matching your interest in business or profession accordingly. You can even study as per choice through distance education (correspondence) using the current time for business or job.

You have already done B.SC ( regular) in 2010. And again want to do a BA (English) from a private university. You can do BA again, it doesn't matter how many times you are doing BA. But one important thing is, It should be from UGC recognised university. Then, you can apply anywhere for teaching posts. Your BA and BEd certificates would be valid. No one would object to It. As mentioned above, you have already done MA so you can continue further study PhD. Then, you would be eligible for lecturer posts in government as well as private colleges.

Whatever courses you are likely to take up for the improvement of your qualifications, there would not be any issue but keep this thing in mind that you need a better concentration in the stream which you you like to pursue. Apart from you are required additional time for the completion of the course. Now coming to your issues relating to question no -1, you can take up B.A degree in English by being a private candidate if you want to improve your performance. You can have more than two graduation degree provided such subjects were included in your intermediate stage.
Moreover as regard to your second question, your B.Ed. Is not likely to be affected because of fresh initiative of taking up a graduation course since your B.Ed would be supported by your qualification B.Sc which you have already possessed.
For your better prospects you should think of ahead with the acquisition of the doctorate degree in English with some university if you get a chance through the interview of the head of the department of English. Alternatively try for NET if you have the minimum qualifying marks of 55 percent in English and by clearing NET, you would be eligible for lectureship in a government college. If the marks in the post graduation is below 55 percent, you may appear in M.A . in English for improvement purpose.
It is always better to go in for higher qualification matching your interest but first of all make your career first with the qualifications already possessed by you.