LLB

ICFAI, Hyderabad is the best campus among all the campuses of ICFAI. The average placement package is 6-10 LPA.

Yes, you are eligible. But you must score 50% marks in your graduation.

CLAT exam is only for 12th pass out students to pursue 5 years integrated LLB course. After completing B.Com, you may take the DU-CET entrance for 3 years LLB at Delhi University and LSAT entrance for joining India's No.-1 private law school.

The field does not depend on whether you have done B.Sc. You need to be specific on your interest as every field has a different approach. The basic education would be the same.

You are not eligible for 3 years LLB degree course as it is not equivalent to a graduate degree. You may be allowed by few universities to do 5 years integrated BA-LLB degree provide these universities accept Diploma in engineering equivalent to 12th. You may check with universities which may target.

LLB itself is a professional degree with which you can have career with corporate law firms, business firms in their law department and as independent practicing lawyer. If you are planning to do corporate law then, MBA may be some benefits. But I am of the opinion that if you want to remain as law specialist, you do not require education in the field of management.

Kindly visit the link mentioned below:
https://www.shiksha.com/college/institute-of-management-education-ghaziabad-295

Sure, you can opt for LLB after completing your BA degree even if it is attained through the distance mode but it is important that the University from where you have pursued your BA degree should be well approved by the authories.
Also I would advise you to pursue LLB through the regular mode, from a good institute and to know about the Law institutes offering LLB degree, you may kindly go through the following link:
https://www.shiksha.com/law/colleges/colleges-india