Teaching & Education

Are looking for lateral entry admission? I would request you to get in touch with officials for details: http://singhaniauniversity.co.in/.

Yes, you can do 2 degrees simultaneously but through different colleges.

Shri Swaroop Govind Pareek Post Graduate College of Education,
S. S. Jain Subodh Women's P.G. College of Education
and
Siddhi Vinayak Teacher Training College.
These colleges offer NTT and B.Ed courses.

The course fee is around Rs 50,000 pa to Rs 70,000 pa.

No, that will not be possible. Your degree must compliment with the post you are applying for.

There are many universities like Annamalai University, Indira Gandhi National Open University, Symbiosis University. Do check the eligibility before applying to any of the university.
Pursuing any course through distance education will be beneficial only if you are working or having work experience.

There are diverse job opportunities available for B.El.Ed graduates.
Common recruiters for B.El.Ed are schools (private, government and community run), NGOs, nursery, daycare centres and tuition classes.
B.El.Ed. graduates may go for roles like Teacher, Assistant Teacher, Instructor, Tutor, Student Counselor and Curriculum developer.
You could even do M.El.Ed which would further your avenues.

Yes, you can get admission in B.Ed. The minimum eligibility to apply for UG courses at Singhania University is class XII pass from a recognized university/board or equivalent.
Admission at Singhania University is done through entrance exam as well as on the basis of merit.

To continue in teaching you can enroll in a B.Ed program. The second option you have is, get a decent Master's degree like M.Tech and write an entrance exam like NET, SLET which will make you eligibility for lectureship and you can see yourself placed in teaching engineering or degree college. You can also apply for Government Teaching Vacancy.