Class 11

Research can be done by anyone. There is no boundation of qualification. In some areas you may need some special permission from concern authorities otherwise you can pursue research on your own.

It is good that you have clear and defined career goals. You may take humanities subject in 10+2 and opt for BA LLB degree. You may appear for CLAT conducted by National Law Universities to seek admission in 5 years integrated law degree after 10+2.

I will prefer CBSE as the study load is slightly less as compared to ISC and the quality of questions asked in the exam is better than the state board papers, thereby, aiding JEE preparation.

There is no particular stream to be taken for becoming a lawyer even science stream people can join LLB. But in my point of view, if you want to become a corporate lawyer then you should choose commerce stream.
If you want to practice in court (litigation) then you should choose arts.
Choosing these streams according to what you want to become will give you in depth knowledge about each subject and enhance your skill efficiently.
All the best.

You can become a nutritionist if you have studied physics /chemistry /biology /home-Science or any two combinations of subjects till your 12th class.