LLM

You can go for criminal law or cyber law.

No, refer the following link:
https://www.shiksha.com/law/course/ll-m-school-of-law-ajeenkya-dy-patil-university-lohegaon-pune-244264

No, there is no entrance exam for the admission.

To become a lawyer you can go for a 5-year course i.e. BBA. LL.B. This is an undergraduate course or you can pursue a 3-year course i.e. a simple LL.B. degree after graduating. After which you can take up the BAR examination.

BHU is not providing distance education and don't have the policy about this. You have to attend your classes as a regular student. On the ground of your job and locality, BHU administration may not allow.

For admission in LLM, you need to have completed LL.B. And also need to appear for NIMSEE exam.

Amity University, Mumbai is one of the best universities in India. Amity University, Mumbai for Law is a very good college. The curriculum for LLM is very well framed and the faculty is also very well experienced. This university has very well inherited its prestige as one of the very good law universities in India. This year alumni are expected to be place with top notch law firms, corporate offices and in private sectors e law students.