CBSE 12th

To get admission in NIT colleges, you don't need to appear for SAT you need to appear for JEE Mains examination, check out the details below:
https://www.shiksha.com/b-tech/jee-main-exam.

Hi,Yes, it is absolutely fine to pursue the integrated course. But, it really depends on the college from where you pursue the same. Thanks.

Yes, you can go for it.

In my opinion, you can do BBA LLB, and Honors course like chemistry Honours, physics Honours, Biology Honours, and if you want to go for UPSC, you can choose BA Programming that is Bachelors in Arts.

Hi, you can definitely take admission for BCA regardless of subjects you have taken in your +2, but I think some institutions mandate maths in +2.

Yes, you can further study Bachelor's course in fashion.

Your marks are really low of the previous, as you have mentioned, it is hard for you to get into XAT colleges.

Do through study of the textbook and get acquainted with questions on it, that's it.

Hi,
That's a good ambition to have and work hard. Keep it up. So, yes once you have your 12th class results out, based on interest and skill set apply for undergraduate programs. Pretty much all fields will help you earn well if you have good abilities so yes, choose subjects in which you are good at. I would personally say engineering and IT, telecommunications, data analytics and data sciences, accounting and banking fields, financial engineering, supply chain management, international business and client interfacing related roles surely boost your pay.

I strongly recommend your sister to please continue her Bachelors in her programme of interest and skill set. Her marks are excellent in PUC and hence Bachelors will boost her profile and confidence. Alongside, she could do part time jobs which can improve her hands on experience and support her financially to become independent. Indeed, Glassdoor, Monster, Naurki are good places to track part time jobs. Just ensure to check eligibility though and then apply for real time projects and summer offers for students.