Punjab

Firstly, you need to have the documents which prove that you are the only daughter of your parents.

Hello Ayush Garg,
Fundamentally speaking, Tamil Nadu gives admissions to engineering colleges to the 'natives' and this is done through TNEA. I am attaching a link that will give you all the required information:
https://www-shiksha-com.cdn.ampproject.org/v/s/www.shiksha.com/b-tech/amp/tnea-exam?amp_js_v=a2&_gsa=1&usqp=mq331AQCCAE=#referrer=https://www.google.com&_tf=From %1$s&share=https://www.shiksha.com/b-tech/tnea-exam

It's not compulsory, however, it depends on the college norms.

From BMSCE Bangalore, SVUCE Tirupati, and GNDU Amritsar for B.Tech in CSE department, I'll prefer you to opt for the BMSCE Bangalore as this is the best college all in terms of placements, infra and faculty.

B.Sc general courses admission are done through online Centralized Admission process. For more details visit www.dhe.chd.gov.in
Eligibility: - A student who has passed + 2 from State Board/CBSE /ICSE/ or any other recognized Board/ University with 40% aggregate marks shall be eligible to seek admission to BSc Semester I. The admission shall be made on the basis of Punjab University rules.
The cutoff percentage for this college is goes too higher, hence your admission chances are moderate.

Please visit this shiksha.com link on B.Sc in interior designing:
https://www.shiksha.com/design/interior-design/colleges/b-sc-colleges-delhi-ncr