LLB

If you do not get college of your choice for 5-years intergrated law degree program then you may do BA or BBA degree courses. On completion of graduation degree, you can do 3 years LLB degree course in any of the legacy universities.

Yes, you can go for 3 year LLB.

All top NLU are govt colleges and you have to appear for CLAT enterance to be eligible for admission.
The admission is strictly based on merit of CLAT score. Minimum qualification is 10+2 with atleast 45% and maximum age should not be more that 20.

To become a professor you need to clear UGC NET, therefore you can focus on completing your law and alongside pursue some part-time or freelancing job.

MBA Marketing and Operations is a sufficent qualification for a good job and career growth. If you do LLB now, you will spend three years in degree. If you take into consideration opportunity cost and return on investment, financially it is not a profitable decision to do LLB now. If you do LLB by distance learning, then you cannot practice in court. Therefore, unless you are passionate about becoming a lawyer, you can evaluate dropping LLB study.

After BA LLB, you can become a Solicitor or a lawyer in consumer, labor, taxation, banking, trademark and patent, criminal, civil etc.
After LLB, you can also take magistrate exam or you may apply in law firm as an associate.
You can also be an consultant in banking, office, etc.