B.Ed

Yes, you can apply for in MDU for B.Ed 2 years programme.

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, Bangalore University does not offer B.Ed course.

Please contact the Institute for fee details.

Yes, you can teach classes upto class 12th after you have completed your B.Ed.

Please refer to the link provided below for an exhaustive list of colleges which offers M.Sc. In chemistry. There is a pool of 405 institutes in India which offers M.Sc. Chemistry, and you can navigate to a college of your choice using the filters on the web page. https://www.shiksha.com/science/colleges/m-sc-chemistry-colleges-india.

For distance B.Ed a candidate must have passed Bachelor's degree with at least 45% from a recognised university. Some of the best colleges which you can try for admission are given below:
Andhra University School of Distance Education, Visakhapatnam, Andhra Pradesh
Annamalai University Directorate of Distance Education
Bangalore University Directorate of Correspondence Courses and Distance Education
Bharathiar University-School of Distance Education
Bharathidasan University-Center for Distance Education.

Please mention the name of the college where you wish to apply.

I don't think so that there is any such option of choosing an additional paper. You need to follow the course structure given by the university.