Hindi

Yes, you can go for Master of Arts (Hindi). To know about the eligibility, please refer to this link:
http://www.ignou.ac.in/ignou/aboutignou/school/soh/programmes/detail/4/2.

English plays a very important role in getting selected for the position of cabin crew.
Cabin crew form the face of the airline and they deal with a variety of passengers who may or may not know Hindi.
Hence a good command over English is essential. Infact knowledge of some other foreign languages like Arabic, German, French etc. adds to the calibre of a cabin crew.
You must improve on your English by taking some classes, only then you can expect to get selected for cabin crew position.
Good Luck !

The medium of CTET paper is bilingual. And you have to choose two languages in paper.

Yes, you can. Wherever the degree of Graduation is required, you can use it there. In both the government and private sector, you can use this degree.

JNU Entrance exam paper will be easily available through Google. The papers can not be posted here as there is no option to do so. You can Check the website of JNU for papers too.

Yes, you can take IPM exam with Hindi. Good luck!

As the exam and the college curriculum is totally in English, you should first work on your English and improve it a bit and after then, try to study English notes, it will help a lot in improving your English.

No, the medium is English.

Most places do not offer History in Hindi. I will try and look up any for you. However, some places can allow you to answer in Hindi.

Take the language that you are comfortable with. It will not matter. You can attempt the paper in both languages too.