Teacher eligibility

Not only a primary or high school, you will be eligible for a higher secondary school. Also, to be a physical education teacher after completion of BPE or B.P.Ed.

Yes, you are eligible but you need to complete B.Ed till next year, if you are being selected in any of the tests.

To become a teacher in a government school, you have to pursue graduation and then B.Ed from any recognised university. After completing B.Ed, you can apply for different vacancies and entrance test and based on the entrance test, you can become a government teacher.

Yes, you are eligible to apply.
For details refer:
https://www.shiksha.com/teaching-education/course/post-graduate-diploma-in-teacher-training-education-all-india-institute-of-management-studies-mandaveli-rd-chennai-24873.

You have completed your graduation and Masters in commerce. Definitely, you should have enough command in your subject. It will be more convenient to you to apply for commerce subjects. But, if you have enough confident in English, and you think that you can carry the subject, then you can apply for English subject.

Yes, you are eligible to become the lecturer of political science subject.

The minimum criteria is-
1. Graduate or equivalent Examination with concerned subject as optional subject and Degree or Diploma in Education recognized by National Council for Teacher Education
2. Working Knowledge of Hindi written in Devanagari Script and Knowledge of Rajasthani culture
For more, you may visit then link below-
http://rpsc.rajasthan.gov.in/PDF_Reports_Files/Detail_Teacher_Gr_II_Elementary2013.pdf

Most universities require English professors to have, at the minimum, a Masters degree in literature. With a Masters, you can teach students pursuing an associate or Bachelors degree, but you will need a Ph.D. in literature to teach graduate level students. If you hope to enter a career as a professor of English literature, knowing the general courses you need will help guide your studies.