Science

Yes, it is directly proportional.

No, not at all. Maths is not required.

No, it is not compulsory.

In order to teach the students of class 5-12th, you need to qualify TET exam.

There are many courses after HSC in PCM. If you are interested in doing something for your nation, you can apply for navy or army. You can also do pursue B.Sc in a particular subject, and further you can opt for Ph.D in that subject. If you are going for B.Sc then opt for physics or mathematics.

All option in front of you are very good. Formal engineering education such as lateral entry B.Tech is the best option. In case you are unable to continue formal education due to personal reasons then you may opt for AMIE.

You have to clear class 12th to get admission in any degree for undergraduate so first do that from NIOS. If that's not possible then look for Diplomas in interior designing after 10th in any polytechnic institute in Mumbai.

Careers options for a science student depend on the research output. Publication of research papers of high quality in reputed journals will surely build up a good career. This is in addition to Ph.D.