BBA

Here are the details of the courses offered by this university. Kindly follow the link to get more information:
https://www.shiksha.com/design/fashion-design/course/diploma-in-textile-and-fashion-design-institute-of-distance-education-university-of-madras-chepauk-Chennai-289765

Hi aman. Kindly visit the link. https://www.shiksha.com/bba/articles/integrated-mba-programmes-in-india-blogId-15044
Good luck!

There is no entrance exam for getting an admission.

Yes you can choose. It's better you should join in any private colleges or in any deemed universities. Because they will provide you good opportunities after completion of your education.

Yes, you can do it. After the completion of intermediate, you can choose BBA. After completion of graduation, you can write ICET entrance exam and you can choose MBA. Some private colleges and some deemed universities and some government colleges provide integrated courses within the span of 5 year BBA+MBA.

You have following options after BBA except for M.A.
(a) 3 years law degree I. e. LL.B.
(b) MCA (if you had Maths in class 12th as a subject)
(c) Masters in Social work
(d) M.A. Mass Communication(e) Join a government job where the eligibility criteria is graduation degree.
(f) Appear for CDS to join defence services.

Hello Jahnvi
Accommodation manager. Catering manager. Chef. Event manager. Fast food restaurant manager. Hotel manager. Public house manager. Restaurant manager. The best colleges in India for Hotel Management are:
IHMCN Delhi, WGSHA Manipal, IHMCTAN Mumbai, IHM Bangalore, IHMCTAN Hyderabad, BCIHMCT Delhi, LPU Punjab, IHMCTAN Chennai, Christ Bangalore, AIHMCT Bangalore, IHMCN Lucknow, IHMCTAN Bhopal. Thank you.

Kindly visit the link. https://www.shiksha.com/accounting-commerce/colleges/b-com-colleges-Hyderabad

The eligibility criteria of BBA in Marketing management of St. Peter's College, Kolkata is given below.
Eligibility criteria : 10+2 or equivalent or have completed 18 yrs. of age & has passed the eligibility or entrance exam. of the University.

No, you will not continue from 3rd year, you can start it from where you stopped it.