Colleges in Karaikudi

If you are from a reserved category, then yes, you can apply for admission here but if not, you are not eligible. Minimum eligibility for admission in PG courses is 50% in Bachelors degree in relevant subject.

Yes, an engineering graduate is eligible to apply for B Ed course.
But, for that you have to qualify the TET entrance exam. The eligibility criteria for B.Ed course is, class 12th with 60% or above, Qualify TET exam. There is no need of engineering graduation to apply for B.Ed.

The bar council has removed age limit for the course but you have 40% marks which is 5% lower than the required percentage. Try doing it from an open university. If you don't get admission, then you either you will have to do another master/bachelor course or a 5 year LLB on the basis of your class 12th percentage.

Use this
https://www.shiksha.com/mba/tancet-exam-cutoff