Direction Admission Process

Which university are you asking about? Amity University Noida (Amity Institute of Organic Agriculture) offers B.Sc. (Hons. ). Agriculture without entrance exam. So you can apply here if interested. The eligibility criteria and selection process are given below. Eligibility criteria : 10+2 with PCB / PCM / Agriculture (min. 55%)
Selection criteria : For the time being Selection Process is based on video responses to the questions posted through the VIDEO LINK available on Admission Microsite.

As per the eligibility for M.Tech, you must have done either Btech or (Bsc+Msc), then only you can apply for M.Tech program. Since you have done B.Sc in Biotechnology, you further need to pursue Msc in any specialisation of Biotechnology
Yes, you can do m.tech after b.sc in maths. sit for gate, score good and get admission to the college of your choice.

It's not possible. In order to get admission in any of the B.Tech programmes you need to appear for VITEEE exam and upon good rank you have to take part in counselling to get admission.

The best private colleges after IEM, Heritage and Techno are (not according to the rank):
UEM-Kolkata,
St. Thomas' College of Engineering and Technology - STCET,
BBIT-Budge Institute of Technology,
Guru Nanak Institute of Technology-GNIT,
MSIT-Meghnad Saha Institute of Technology,
CIEM-Calcutta Institute of Engineering & Management, FIEM-Future Institute of Engineering & Management,
MCKV Institute of Engineering-MCKVIE
BP Poddar Institute of Management and Technology.