Dual

You can apply for NET exam. If you qualify that, you can become a lecturer.
You can start your own business.
Or you can work in any company.

Regional Institute of Education is one of the college offering integrated programme. For details refer: http://www.riebbs.ac.in/4-years-b.sc.b.ed.php.

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Please go to the college predictor link I am sharing to know the college you can get. Good luck.

https://www.shiksha.com/science/course/integrated-b-sc-hons-m-sc-hons-in-mathematics-maharshi-dayanand-university-rohtak-270937
I am sharing a link here. You go through the link here. You will get all knowledge about MDU campus.
Good luck.

Yes, through JAM.

Yes, definitely after M.Com if you want to pursue B.Ed then it will be of two years. Also B.Ed is a two year training course but some university, college and institute has integrated programme for this course. Like. Regional institute of Education, Central university of south Bihar.