Teacher

As it is not a regular job, it depends on the requirement they feel for the subject. If they can't find anybody else, they will pay you more. Or else, they pay less.

There are so many universities or group. You can find out about their placement, history, salary, past year results and other information. Talk to some expert and then decide.

You need to go in for B.Ed or ecced to teach primary section. B.Ed to teach upto 12th standard in secondary section. D.Ed to teach primary section. govt aided school ask for D.Ed in primary section . age to.apply for D.Ed is below 35

Amity Institute of Education
Army Institute of Education
AURA Institutions
B. K. Institute of Education & Technology
C E S College of Educational Research and Training
Central Institute of Education Delhi University
College Of Education, Delhi University S
Department of Education Shri Lal Bahadur Shastri Rashtriya Sanskrit Vidyapeetha
Excel Institute of Management & Technology
Faculty of Education - University of Delhi
Guru Gobind Singh Indraprastha University
Guru Nanak College of Education
Guru Ram Dass College of Education
Indira Gandhi National Open University
International Women Polytechnic
Jamia Millia Islamia

In school teaching engineering is not a subject therefore it is not included in the list

Dear Subrata,
A year loss for MAT exam will affect because for clearing MAT exam it takes less than a month preparation, but if you are graduating this year and targeting admissions in next year I suggest you to prepare for CAT/XAT/SNAP/IIFT because these exams carries value.and if you manages to score anything above 85% then you will be getting in top 20' business schools.
All the very best.

You can become a Teacher with any subject that you have.