India

Yes, you can go for MBA in energy and environment stream. Prepare well for the MBA entrance exams. A good score in CAT will make you eligible to sit for top institute's selection process. SIIB is one of the good institutes offering this course.

Hi Dharani,
UEI Global is India's top hotel management institute, associated with Hotelschool, The Hague (World Rank amongst Top 3), to provide International Certifications to all the students. At UEI Global, in addition to UGC recognized degree, the students will get certificates from sector skill council which will also help to integrate internationally. Kindly, visit the campus for proper career counseling.

Yes, you can always apply for higher studies abroad. You have to appear for the entrance to get eligible for admissions abroad. Visit the university's website to know about the eligibility criteria.

Hi,
BBA can be done after class 12th. There are many colleges (government and private) offering this course. Not sure which city you are in, some of the good universities are DU and JMI. There are some major government colleges too. In private universities, Amity is good. There are many more options available. Admissions are based on class 12th marks in some colleges but mostly are based on entrance exams.

If you are talking about tuition fee of INR 5 lakh then Hindustan University and SRM stand at the top followed by SASTRA University.

All the cities you have mentioned have the best of colleges for MBA. Visit this below link for the list of top colleges in India:
https://www.shiksha.com/mba/colleges/mba-colleges-india