CBSE 12th

American Universities don't see only SAT and TOEFL scores. They are interested in whole personality. They see your academic record, extracurricular activities, essay SAT and TOEFL score. You have to do your best in all in these factor.

If you're interested in IT and software then you can choose engineering. You can give JEE Mains exam and according to your rank, you can get the best college.

There are a number of good universities that provide direct admission, the minimum requirement for BBA is 50% in 10+2 (with English). You just have to research which are the college that provides BBA and what is the procedure for that particular college. You just have to visit college website, you got an idea about the admission process either you can apply online or offline. List of some colleges for BBA:
Lovely Professional University, Jalandhar
Birla Institute of Technology and Science, Pilani
Motilal Nehru National Institute of Technology Allahabad
Ramaiah Institute of Technology, Bangalore.

If you want to teach the students interested in the preparation of IIT there is no restriction that you have to choose B.Tech or B.Sc. You can do either one of them. There are many B.Tech holders who are even pursuing M.Tech and becoming lecturers. So it's up to you in the field you are interested. technical or non-technical.

It is compulsory to have maths in +2 to be eligible for admission since SRCC offers only honors courses and hons courses require maths.

Usually, a minimum of best of four 97.5%/97.8% is required. That's the minimum. Scoring a 98 or above would be on the safer side.
Maths is required as one of your subjects in +2, and you need to pass in it. However, it's usually not calculated in the best of four.

If you want to qualify NEET, you have to study hard in class 11 and 12th. Also, I would recommend you to take coaching and focusing on NCERT syllabus.