LLB

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.

You can definitely prepare for CLAT while studying.

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.