Science

No, lateral entry is not allowed in this college.

Yes, if Bachelor in Library and information Science is a part of college and every part of the college has equal rights to participate in fest and function irrespective of the batch, year or state. So, you would definitely get an opportunity to see fest, societies and events.

Fill online form and give entrance exam after that, you will be able to get admission.

It depends on college to college whether they accept NEET or any other score but most colleges give weightage to NEET score.

The details about the course, fees and other details about the course is given in this link. https://www.shiksha.com/college/national-college-of-design-ncd-chennai-egmore-26933/courses

CUSAT has extended their application form two times. The last date was to fill the application form was 31st March. Now it's over. I would recommend you to search for the similar and best college which provides similar curriculum as CUSAT. It will help you to save your one year of life or if not, stay alert for the next year application.

The SSCBS entrance test is open for both Maths and non-maths students. But being from a Maths background is preferable as the entrance test requires decent knowledge of Maths upto class 12.

Here is the list of few colleges-
Guru Gobind Singh Indraprastha University, Delhi.
Symbiosis International University, Pune.
Christ University, Bengaluru.
NMIMS University, Mumbai.
Bharati Vidyapeeth Deemed University, Pune.
Gitam University, Visakhapatnam.

Yes you can do Maths in first year and then choose whatever subject you want after that

Kindly see the below link for information related to your query.
https://www.shiksha.com/college/indian-institute-of-fashion-and-design-iifd-chandigarh-48504
Thank you