Kerala

It's not possible. It's not school. You can't switch it to continue with some other college. So, it's not possible.

Hi,
Admission is through Tamil Nadu Engineering Admissions (TNEA) counseling based on the marks obtained in 10+2.
Interested candidates can apply online or offline with the required information.
https://www.shiksha.com/b-tech/course/b-e-in-aeronautical-engineering-madras-institute-of-technology-chrompet-chennai-167411

Hi,
I believe that you have finished your class 12th/Schooling after which you took a gap of a year and you wish to join college now. There will not be any problem in applying to college. Just make sure that you check the prospectus online and read the guidelines before applying to college. In general there is no problem at all for dropper.

Any government college will be charging less than 2 lacs per annum in not only your mentioned states but in any state in the country.

You need to clear NEET and once you have qualified NEET, then look for your preferred colleges, check out their websites, and you can then know the criteria required to get admission there. Private colleges usually don't have a domicile issue.

There are no such common exams. Most of the colleges in Karnataka offer BBA upon direct visit and submission of application form. In case of a large number of students, seats are allotted on merit basis. However certain colleges mandate a general entrance exam for joining BBA course. You can search in the website for such colleges and find the exam dates. These exams mostly have centres in Kerala (Cochin and Trivandrum mostly). One such college is PES University, Bangalore.

Nope. No good colleges do that. Even if there are colleges they might not be approved by AICTE or NAAC. This is a huge risk and mistake and it will turn out to be waste of 4 years after the completion of your course. Your course will be invalid.

Sorry. There are no options. CET Trivandrum is a government college and admissions to all government colleges are through allotments based on Kerala entrance score. Also, any engineering college in Kerala mandates a min score from Kerala entrance exam.