LLB

Yes, almost every NLU offers this course.
Check the websites of the respective college for courses offered by them.

However, you can also opt for Campus Law Centre, Delhi University for the same.

Dear,
According to your statement, you are still in confusion regarding your further education or career path. If I recommend any programme, that will not be right.
According to me, you should go for career counselling session with renowned career counselor and discuss all the factors and then choose the right path for your future.
All the best.

You need to take The Bar Council exam to start your practice at any court. You may need certification from any state of the State Bar Associations for practicing in a particular state and also appear for All India Bar Council Exam, later on.

Eligibility criteria for doing 3 years LLB degree is graduation degree. As you are still doing your graduation degree, you are not eligible for doing LLB.

If you want to go for LLM, why don't you take CLAT P.G. entrance and get into a National Law University for this purpose.

All sections are equally important to crack a good college. Apart from that, focus on your weak areas.

Dear
LLB is a law programme that you can pursue after graduation and you can do practice after getting the License from Bar council of India.
Yes, you can pursue LLB programme from any graduation degree and duration is for 3 Years through regular mode only.
You can apply for CLAT and individual entrance exam of different universities for Admission in LLB programme.
You can check this link for top law colleges in india and you can do the comparison too.
https://www.shiksha.com/law/ranking/top-law-colleges-in-india/56-2-0-0-0
All the best.

Dear,
As per the guidelines, LLB programme will be a regular mode and as you have a government job, how can you manage your work schedule with a fulltime course.
So, choose the programme considering all the factors.
All the best.

Dear,
Yes, you can pursue 2 different programme from 2 different university in regular and distance mode.
LLB is a fulltime course so accordingly you can pursue MA as distance mode with IGNOU.
All the best.