B.E.

I think, once you are done with your graduation, you can go for Diploma in Airline and Airport Management- for a UG degree and then try for MBA -Airline Airport Management. UG-
https://www.shiksha.com/aviation/ground-services/course/diploma-in-airline-and-airport-management-aimfill-international-jayanagar-Bangalore-179441
PG-
https://www.shiksha.com/aviation/articles/mba-airline-airport-management-blogId-3783.

I think, for such specific detail, you can get in touch with your college as they will be the right party to answer your question. But, I think that you can retake admission in the course and there shouldn't be any problem/challenge about the same. I would still suggest you to talk to the college management/university management for reconfirmation.

Eligibility criteria for M.Tech Naval Architecture is:
Bachelor's degree in Naval Architecture/ Marine Engineering/ Nautical Science/ Ship Building/ Mechanical Engineering/ Civil Engineering/ B.Arch or the equivalent.

Yes, there are chances that you will get this college. I have friends who are studying in that college. For more details comment below.

Yes, you may check out the website http://www.oriental.ac.in for the same updates if any. You may drop a mail related to that along with the CV and the post you want to apply for at oistbpl@oriental.ac.in. At last, you can make a call to the college and enquire for the same or directly walk in. Hope it might have helped you.

The fee for B.E. in Automobile Engineering is around Rs. 1.5 lakh.

Register and Apply:
Interested candidates can apply online with required information.
Counselling
Admissions is through Tamil Nadu Engineering Admissions (TNEA) counselling based on marks obtained in 10+2.

Admission in this college requires MHCET score as well. Also, for pursuing engineering a minimum of 70% is required in PCM.

You don't require mathematics as a main subject in order to pursue B.Sc in Economics. But, for B.Sc in Mathematics and Statistics you need Mathematics as a main subject in 10+2.