Chinese / Mandarin

JNU will release the exam notification when the forms are out. You will then get admission on the basis of your result.

Yes, you are eligible for Bachelors in chinese course. Good luck.

Perhaps, you can pursue B.A. In Chinese (private) or from an open university or through distance education. It is better to do certificate a and after that, Diploma in Chinese. Some universities / colleges provide certificate course in Chinese after 12th. So, you can take admission in that. These are part time courses. So, you can continue with your graduation.

If you even have a bit of understanding of English, French will be much easier to grasp. Both have nearly same alphabets and grammar rules. You can also understand the scripts for both. Chinese and Japanese are a total different matter altogether. Their script is different and there are several versions of the language. Chinese is much difficult in both because of its number of characters that are over 10,000.

Chinese language BA. It is the best you can think of. With trade growing by leaps & bounds between India & China, there is an acute shortage of Chinese language experts in India. Translation is only the top of iceberg. Go ahead.
Best wishes.

Visit:
jmi.ac.in
Open it regularly. The dates can be out soon.
All the best.

You can prepare according to Syllabus, you can find the syllabus from this link:
http://jmi.ac.in/studyatjamia/Syllabi/entrancetest.
You can prefer various books like Arihant preparation books etc.