Class 11

Unfortunately, the selection of subjects in class 11th are based on the percentage of SSC exams. So, based on your Maths and Science percentage, you'll get Science stream which have options PCM and English, Biology, biotechnology etc. And rest commerce and is based on lower the percentage of SSC exam. So, selection of subject is done by school only on the basis of class 10th percentage. Regards

If you don't have 10th pass degree, you can't pursue 11th in any stream because the institute demands 10th class all certificates.

Now, you have to work hard in 12th class. If you score well, you can take direct admission.

It depends on her interest. If she likes to study science in 10th class, then she can opt for science or if she interested in maths, then she can opt for commerce.

I think you should choose PCM group because with PCM group you get more options in your graduation.

https://www.shiksha.com/humanities-social-sciences/ranking/top-arts-colleges-in-Pune/95-2-0-174-0
Here are some top colleges of Pune.

Girijaprasad Sharma,
You need to attempt JEE Mains and Advanced exams. After qualifying in Mains, you need to attempt Advanced.
There, you must get a rank from 1-5000 then you can study in IIT and that too engineering.
All the best.