Teacher

You can do the B.Ed through distance mode from open universities.
Good luck.

If your B.Ed is done from a reputed institute, then it is valid all over India.

Eligibility for Annamalai University.
Eligibility: Candidate must possess B.Ed or M. H. Ed degree with 50% marks from this university or any other recognized university but for SC/ST candidates must pass in qualification examination. Hope this helps.

Yes, you can get a job, if you have specialized in drawing.

Yes, Chandrakala you are eligible to apply for the Post of an Assistant Professor as per the rules of NTA there is no age limit for Assistant Professors. But you are running on the last age limit criteria to apply for the JRF, the maximum age limit to apply for the JRF is 30 years. If you wish to apply for the UGC NET Application form for the June session are out and the last date to fill the form is 30th March 2019. You can fill the form from the official website of NTA https://ntanet.nic.in/ntanet/root/loginpage.aspx click on the given link to fill the UGC NET Online Application Form.

In private schools CTET is not mandatory. It depends on the selecting authorities.

To choose teaching as a profession, but not becoming a school teacher, you have to do postgraduate course and then UGC NET. And then, apply for lecturer or professor post.

Yes, you can do pursue MA in social Science after completing B.Sc.

No, to do B.Sc only, it doesn't mean to be a teacher. Now, in private schools, you have to do a bridge course in education.

Yes, it is a good option, but after your B.Sc pursue B.Ed from good college and clear government exams to be government appointment, or you can also directly join into a private school.