CCSU - Chaudhary Charan Singh University

Not all private colleges grant admission in the 2nd year. You first need to decide on the college and check if they have any such provision of granting admission in the 2nd year. Admissions also depend on the availability of seats.

For Chaudhary Charan Singh University, there is no entrance exam required.

No,
You should not apply for the reservation seat as you do not have your caste certificate. As when the colleges check your documents, it will be a great risk for your candidature in the college. Therefore, it should not be the option for taking admission, as you don't have any proof.

The course offered by the university is MA in Hindi. They do not offer Hindi Literature.

For fee details, please contact the college authorities. Visit the link for details: http://www.ccsuniversity.ac.in/web/Contact-us.htm

Can you please elaborate what does private mean?

It is possible, but the college should be affiliated from the same University in which you are studying.

Nobody can say correctly. At first, you may reach in PG, then qualify next try for job. Your dedication may prove your success.