BBA

You can consider following colleges:
1. BLS Institute of Technology Management
2. Delhi College of Advanced Studies
3. Delhi institute of Rural Development
4. Don Bosco College
5. Goa University

Yes, they can join BMS College for doing part-time B.Tech in ECE.

No, you don't need to go in formals.

Sorry but no one can give you the details about vacant seats. You have to ask official authorities about the same.

The forms will get released in June.

The fees would be around 27000 per year.

Hi,
Admission is based on the marks obtained in 10+2. Interested candidates can apply online/ offline with the required information.
https://www.shiksha.com/bba/course/bba-in-airline-and-airport-management-skywings-academy-of-aviation-and-tourism-kochi-253052
https://www.shiksha.com/bba/articles/your-c

Yes, of course. You can get admission in MIT. But, I would suggest you to be well prepared for the entrance exam which is conducted for the admission process. It is not tough but to be prepared in well advance will always result to be beneficial.

Practicing mock test is the best way, as it will boost your confidence and you will have a clear idea of exam pattern and will have a good command on paper. All the best.