Law

The top-most Law entrance exam in India is considered CLAT (Common Law Admission Test) because it provides admission to the NLUs in India. After CLAT, AILET (All India Law Entrance Test) is another top exam conducted by NLU Delhi. SLAT (Symbiosis Law Aptitude Test) is another exam to offer admission to the UG Law programme at Symbiosis.
Apart from these, CUET, CUET-PG, APLAWCET, TSLAWCET, TS PGLCET, etc., are also conducted for Law courses at the state level. 

Yes, you can, but it's not worth pursuing, at least in India. The Bar Council of India it's a regulatory body for legal education in India, does not recognize any distance or online degree to practice Law as an Advocate in Indian courts.
A distance or online programme can only give you a flexible learning option, but in my opinion, it's a waste of time and resources if you really want to become an Advocate in India.

The LLB course duration is 3 years; however, if you plan to pursue a BA LLB, BCom LLB, BSc LLB, or a BBA LLB, then the course duration will be 5 years, that is, 3 years general course + 2 years LLB.
Now, talking about the structure, you'll study almost every Law specialisation on a basic level. For instance, Constitutional Law, Criminal Law, Contract Law, Property Law, Tort Law, Family Law, Jurisprudence (legal theory), International Law, etc. 

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BA LLB

There are countless. You can become a practicing lawyer based on the Law specialisation you choose, you can join a firm or an MNC as a legal consultant, or take any other job role in the legal department, or you can even join a government department like the Judiciary, PSUs, banks, etc.

Legal Aptitude in a Law entrance exam means, they'll check your problem-solving and analytical thinking, required in the legal field. In the Legal Aptitude section, you'll be given a mixed set of questions from Legal knowledge (current affairs, legal topics), and logical reasoning (comprehension, problem-solving). You will apply the legal principles to the given factual situation. This section will include passage-based questions and case studies. 

The eligibility criteria for mainstream Law courses in India -

• A 3-year LLB requires you to have a bachelor's degree in a relevant discipline from a recognised university.
• A 5-year LLB (BA LLB, BSc LLB, BCom LLB, etc.) requires you to pass Class 12 from a recognised board; the stream can be any.
• For an LLM, you're required to have an LLB degree, and for an LLD, an LLM degree is required.

Source - Multiple external/ official sites, info may vary.

Taking admission in the BA LLB (Hons) course at NLU Assam is considered a great option. The university is well-known and reputed for the Law programmes offered. Candidates must appear for the CLAT exam for admission in the university. 

Please add these entrance exams also in your list for LLM.

1. MHCET Law LLM
2. LSAT LLM
3. AP PGLCET
4. CUET LLM for DU
5. SLS AIAT LLM
6. TISS LLM Exam
7. PU LLM Law
8. BHU PET Law