CBSE 10th

If you are interested in science then only take it. Don't force yourself to any stream. Do as per your choice and interests as your future depends on it. At times, people take science stream as all others are taking the same. This ruins their interest after some time.
Science will prove to be a bit difficult for you as your class 10th percentage is low.
Explore yourself and take the right decision.
All the best for the future.

Since admissions in engineering/medical colleges on an all India basis are based on central open tests which are based on CBSE syllabus so it's better to study CBSE after 10th.

Hi Shrabanti,
Surely you can get admission into many good colleges, but in order to get admitted to a reputed and good college, you must secure good marks in entrance exam. Doon Business School, Dehradun is one of those institutes which will also provide scholarship to you if you do well in your entrance exam. So buck up and put in your all efforts.

The eligibility depends on the type of course that you wish to pursue, the details of some courses are stated below:
Diploma class 10th pass from a recognised board with minimum 40% marks.
Bachelor's Degree: Class 10+2 examination with at least 50% marks.
Post-graduation degree: Bachelor's degree from a recognised university with at least 45% marks. Graduation and PG programs may also require you to appear in the entrance exams.

https://www.shiksha.com/college/indian-institute-of-management-Indore/exams/ipmat
You can get all the necessary details from the above link.

To study in UK it is important that a foreign student should have completed his/her 12th in his/her own country from a recognised board and after studying in London it is important to appear for IELTS or GRE.

There are a lot many options ahead. Don't choose on the basis of what is currently in demand or what promises to do so. Find what you want to do or rather what interests you the most and then choose the path accordingly. You have a lot many options right now and are prone to feeling overwhelmed. Seek your elders' advice, you don't have to follow them.

Yes, you are eligible for scholarship, but universities will assess your profile and then they will give you a scholarship.