LLB

Hi
No, you can't go for LLB and LLM directly after 12th. So, options available to you are:
An integrated degree like BA+ LLB (Hons) or B.A.+LLB (Hons) or B.Com+ LLB. (Hons) depending on your interest. Eligibility for all of these degrees in most of the top universities is pass with 60% aggregate marks in 10+2 and you might have to clear some entrance test (depending upon the university you want to take admission in).
B.A + LLB (Hons): Targeting students with an interest to pursue legal education with social sciences to benefit society. Creation of well trained and dedicated professionals in the legal framework.
B.A.+ LLB (Hons): Graduates may opt for legal practice, where management foundation will groom aspiring lawyers for the corporate sector. So, you can choose any of the above depending on your interest. It will be advisable if you do your degree from a well-known university and that provides prime placement opportunity, outstanding exposure and professional enhancement training.

Hi,
Yes, you can pursue your career in law after B.Sc. The eligibility criteria for pursuing LL.B. Is that you have to get minimum of 50% marks in your graduation degree and you might have to clear some entrance test with it, ( it may vary with the university you want to take admission in)
After LL.B. You can appear for Civil and Judicial services in your respective States. IAS Services, JAGS, services in Army, Corporate Lawyer, Legal Advisors in MNCs and Company, Legal Processing outsourcing, Practice in Criminal, Civil or Income Tax as an Advocate. It will be advisable if you do your degree from a well known university that provides prime placement opportunity, outstanding exposure and professional enhancement training. I can enlist some university for your help -
Symbiosis University, Lovely Professional University, Aligarh Muslim University, Christ University etc. Are the prime names offering all these assets to their students. These universities provides extensive learning programs and exposure to the students. They also provide worthy scholarships to its students depending upon the entrance test taken of the university or board result.
I hope it helps.