Colleges in Tamil Nadu

Yes, you can apply for distance courses. The gap year don't matter in distance courses.

Here is the list of top colleges in India offering B.Tech in Aerospace Engineering:
Park College of Engineering and Technology, Coimbatore
Lovely Professional University, Punjab Engineering College, Chandigarh
Hindustan Institute of Technology and Science, Chennai
Madras Institute of Technology, Chenna

No, NIT, Trichy is not offering this course.

If you wish to join the distance course, the university has different branches in different districts. Look for that and you will get your study materials by post.
Regards.

You need to fulfil the following eligibility criteria in order to seek admission in BE in Aeronautical Engineering:
Candidate must have passed 10+2 along with mandatory subjects from a recognized board/university or authority accepted by the syndicate of the Anna University as equivalent thereto are

Yes, you will be able to get admission in AE. For getting into IITs, board exam marks doesn't matter, the thing that matters is JEE Mains and Advanced score. You should secure a rank under 10000 to get IITs and under 60000 to get good NITs.

Dear friend, as per my opinion and my knowledge if you had done B.Sc with zoology, microbiology, chemistry, medical laboratory technology, biotechnology then definitely you can go ahead.
Good Luck.

These days cut off at DU is quite high. For seeking admission in a good course from science stream you should get 85%in PCM or PCB. Loyala College is a private college, there is no as such high cutoff. If you have above 80% you can get the direct admission. Otherwise, for less than that marks others

No, there is no center available in Bhubaneswar of Annamalai Distance University. There are various universities available for distance learning courses like Amity University, Suresh Gyan Vihar University, Mewar University and many more.
http://topdistancemba.com

Minimum 3 years and Maximum 5 years.