West Bengal

Yes, you have to appear in the entrance examination to get admission in fashion designing.
But there are some colleges which give the facility of admission directly. According to me, it will be better when you go after qualifying entrance test.
Entrance exam for designing course:
https://www.shiksha.co

https://www.shiksha.com/bba/course/bachelor-of-business-administration-university-of-engineering-and-management-kolkata-rajarhat-236632
Please click on the above link to get all details about the college. See whether it is the best college for you after going through all the data of the college.

With rank 14896, you will not get any good branch in Heritage. All I can say is that you'll make the cut for any branch except CSE in NSEC, Meghnad Shah Institute of Technology, also a few branches at TISL, any in TIU and TICT.

You will get Calcutta University for sure. Another college you will get is Jadavpur University but for architecture branch I will suggest you to join Calcutta University because of their faculty members. They are so good.

The total fee structure is 8.65 LPA.
https://www.shiksha.com/mba/course/post-graduate-program-in-business-management-praxis-business-school-praxis-kolkata-24-parganas-south-113953

No, direct admission isn’t possible as you have to get through e-Chat exam to get admission in IIHM, Kolkata.