Delhi University (DU)

Yes, you can get it. As per the year 2019-20, DU cutoff (5th list), the closing cutoff in B.Sc. (Hons) Mathematics in your category was 83.5. Hence you have chances here.

Hi,
After completing your B.Ed, you will have to qualify for the TET/CET exams. After this, you can apply for teaching jobs. For teaching out of India better go for professorship after doing Ph.D. There process is very difficult. You have to be a recognized doctorate by publishing researches etc.

Yes, it mandatory to give JEE Main exam for science student with Maths
https://www.shiksha.com/university/du-delhi-university-24642/admission
Here is the admission procedure to get admission in this college
Kindly follow the link to get complete.

You should go through the prospectus of the course offered by the institute to know more about admission procedure, fees, syllabus, course structure etc. Though for DU fees would be almost negligible.

Here is a possibility of an improvement exam, but you need to go to Delhi university complex examination branch and ask there Take application form. It is in the north campus of DU.

B.Ed is a two-year course, divided into four semesters. You will have to go through the prospectus of the course provided by the college to know more about the admission procedure, eligibility criteria, fees, course structure etc.