Teacher

You are advised to appear for National Eligibility Test (NET). NET is a test to determine eligibility for college and university level lectureship and for the award of Junior Research Fellowship (JRF).

You may become a teacher after your graduation only except few primary assistant teacher vacancies in the state on the intermediate level. First, decide which subject you will prefer after your intermediate. If you want to complete your studies abroad, you may start your preparation for SAT exam which is an entry level test to get admission and scholarship in the universities across the globe.
All the best.

Yes, you can. Also, appear for GATE exam once again.

Dear,
According to your query, my recommendation will be for MBA programme from top B-school because through that you can get the knowledge, skills and management strategy and best placement. Even afterwards if you want to enter into lecturer profession then you can apply for colleges with your Management degree in related domain.You can think of PhD in management for further education in terms of growth.
All the best

Hello Abhishek,
I appreciate your interest in the profession of lecturer in a government engineering college. To achieve the same, you need to clear UGC NET entrance examination. With this, you can apply for assistant lecturer in colleges. However, to be a senior lecturer / professor, you need to complete Ph.D along with minimum 5 years experience as a lecturer.

National Eligibility Test (NET) is a national level exam conducted by University Grants Commission. By qualifying this test, post graduate students may apply for lecturer-ship in reputed universities and may also seek admissions for PhD Programs in Net Coordinating Universities.
The candidates who wish to appear in Net Exam must have fulfilled eligibility criteria declared by Net Coordinating Institutes.
Final Dates are not out yet:
Important Tentative Dates CBSE UGC NET 2017 (July)
Starting date for application process April 2017
Last date to apply online May 2017
Last date to submit fee online May 2017
Examinations Date June 2017

You should complete your graduation in chemistry, and then you can pursue B.Ed. After appearing for TET, you are eligible to teach up to class 12th. For graduation and post-graduation, you have to complete Masters in chemistry and have to clear NET to be eligible as a lecturer.
All the best.

You can do PhD while doing a teaching job.