Trivandrum

It's up to you that which suitable to you. But as your question I suggest IHM Gwalior. But firstly check ranking of institute that you prefer.

Hello Tarun,
I am afraid, the information you are seeking is not available. However, it is expected that cut-offs will be about 5000 rank (JEE Advanced for general category).

Yes, you have a very high chance of getting a seat in CET.
First, visit this link to check B.Arch colleges based upon your JEE rank:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6919840
Then visit this link for various colleges which will provide you the brochure:
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india

There are over 5 Graphic/Web Design colleges in Thiruvananthapuram offering 27 courses.
Check the list of all Graphic/Web Design courses in colleges/institutes in Thiruvananthapuram listed on Shiksha in the link provided below:
https://www.shiksha.com/animation/graphic-web-design/colleges/colleges-thiruvananthapuram

Evening/distance/online/part time engineering courses are not valid any more as per the latest supreme court verdict , hence would recommend you to join regular btech course for better career prospects
http://www.tribuneindia.com/news/nation/no-technical-education-through-correspondence-says-supreme-court/491819.html