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EDIT: Admission to general courses has started. Fill the form quickly. The last date is 24 Nov 2020.
https://nehu.ac.in/public/uploads/Admission-notice-Gen-PG-Ph.D-2020-21.pdf
Hello Seveu,
NO, The admission dates for MA courses haven't been started yet in the university. Last year the last date for general courses was the 16th of July but this time due to this pandemic they haven't started yet. Please check the announcement site of the NEHU portal frequently for admission related information. I'll let you know once they started the process.
link: https://nehu.ac.in/Admission-Announcements

If a candidate satisfy the given below criteria then he/she is eligible for IIT JAM chem exam
Bachelors degree (at least 10+2+3) with Chemistry as a major/honours subject and Mathematics and Physics as other subjects, or
Candidates having a Bachelors degree (at least 10+2+3) without (Major/Honours) must have the concerned degree with (a) Chemistry as a subject for three years/six semesters, (b) Minimum 2 (Two) courses in Mathematics (c) Minimum 2 (Two) courses in Physics
While some demands only Chemistry as a subject for three-years or 6 semesters.

Hello Aditya, firstly for admissions in engineering colleges in Maharashtra, eligibility is on the basis of entrance examination conducted by the government of Maharashtra. If course few seats are reserved for those outside Maharashtra under All India Quota. But these seats are very few in numbers, but filled up based on JEE Mains results. You will get full information on the web page if dte of tech education of the state. Best wishes to you.

Yes, but you must have a master's degree also.