History

Yes, you are eligible

Yes, you are eligible, as the minimum marks should be 50% for BA History.

Best book for paper 1 and paper 2 for Public Administration.

Please mention the name of the course you are interested.

Even your graduation is other than Islamic History. Still, you are eligible to apply for MA in Islamic History course from MANUU as basic requirements for this course is 40% marks in any Bachelors degree or equivalent degree from recognized university.

There can be no problem. The combination of subjects suit. The rule cannot be otherwise.

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.

Kindly specified from where you have done Bachelor's and also your percentage, your subjects in bachelor's degree.

Yes, you can apply for all the posts, which require only graduation degrees, like railway, post office, police, SSC, state PCS, UPSC and many more. For admission in MA, you need to have a graduation degree. Just wait for the notification of the college you want to get admission for MA.