M.A

After completion of your graduation in BA you can go for MA in English literature.

Due to lack of clarity on what is the kind of exposure you have in HR it will be difficult to share advice.
However, you could pursue PhD in HR / English or seek special certification as a host of area in HR/training/analytics.

Yes, IGNOU has international reputation. It course material is of international standards. You can go for it. However, to enroll for MA one should have completed graduation.

Eligibility criteria for Master of Arts (Public Administration) is a Bachelor's degree in any stream of minimum 3 years duration. You are eligible to seek admission in MA Public Administration based on your B.Tech degree. B.Tech is sufficent qualification for seeking Government job.

Every state has its ways of conducting exams for B.Ed and has percentage norms for it. Kindly check with the university in which you want admission.

With MA English you will be sectorial specific and MBA will equip you with wide range of career opportunities. You will be able to go for corporate s where you can fetch fat salary:
www.taxila.in

Please refer to the link mentioned below for the list of colleges which offer M.Sc through correspondence or distance:
https://www.shiksha.com/science/colleges/distance-correspondence-m-sc-colleges-india