Science

Below I am mentioning some famous and easily available books for the preparation of M.Sc Zoology entrance exam. You can pick the book as per your understanding. Zoology A Complete Guide (M.Sc. Entrance Examination) (1969) by Anita Sehgal Dr (Author)
M.Sc. Zoology Entrance Examination A Sehgal. TRB Zoology (PG) Previous Years Model Solved Papers 2017 by S. Devi Parthiban (Author)

Yes, you are eligible for a lateral entry admission if the Diploma is done after class 12th. For the lateral entry admission, eligibility is somewhat equivalent to the requirement of the course. If you have done a Diploma after 10th, that means the eligibility is equivalent to 12th, and you get admission in first year only.

No you can't do B.Com without maths because maths is actually a mandatory subject in the course curriculum. It is applicable everywhere from where you want to pursue B.Com.