Class 11

To apply for the post of professor, you need to have a specialization subject which you can choose during your duration of pursuing UG degree. After all, the institute has different requirement criteria, but majorly they require you to have a doctoral degree with a particular specialization.
Most of the recognized universities require you to have appeared and cleared the NET exam after which you are eligible for the post of assistant professor or State Level Eligibility Test after which you can work with the state level universities, colleges or institutes.

Yes, you can get admission in 12th NIOS.

Go for a diploma course in Photography or else go for a degree course like B.Sc in Media Science/Mass Comm.

Surely, you can as you have physics, chemistry and maths as the main subjects in class 11th.

Yes, you can. Try to check BBA colleges without maths. I think Guru Gobind Singh Indraprastha University, Madras Christian College are other good colleges which allow BBA without maths.

You should do whatever you are passionate about, if you are interested in doing chemical engineering then go for it.

Do Bachelors in India and then move abroad for Masters. The labor put into studies in India may help you a lot. Germany, Netherlands and Norway are great for colleges without tuition fees. The fees and cost of living abroad along with tuition fee may be around 50 lakhs.