Biological Science

Please refer to the link provided below for details regarding a course in B.Sc. (Hons.) in Biological Sciences from Presidency University, Kolkata. You should be able to download college brochure from this link which contains details regarding registration dates for this particular course.
https://www.shiksha.com/science/course/b-sc-hons-in-biological-sciences-presidency-university-kolkata-college-street-271002

Yes, you can. NEET 2018 Exam will be on 06th May 2018. So, not much time left for the preparation. For NEET preparation, you should now only study the most important topics. Solve previous year question papers and take online mock tests. Download previous year NEET Exam Question Papers here:
https://scoop.eduncle.com/neet-previous-year-question-paper
Focus more on NEET Physics section. This is the most difficult section in NEET Exam. Learn all the formulas as they are the backbone of NEET Physics. Make notes of all the important stuff. This will help you in your last minute preparation.

Where do you wish to apply? For apply to B.Ed biological Science you need to have completed graduation (B.A. / B.Sc. / B.Com. ), from a recognised university.

No, it's not compulsory.

Please refer to the link provided below for detailed syllabus of the CUCET entrance exam for PG courses in chemistry:
http://cucet2017.co.in/PDF/Syllabus/PGQP27.pdf
Central Universities Common Entrance Test (CUCET) is an all-India level entrance exam conducted by ten central universities and Dr B R Ambedkar School of Economics (BASE) for admission in UG, PG, and PhD courses offered in these institutions. Central University of Rajasthan, which is the coordinating university for the exam invites applications from aspiring students each year.