Design

Please refer to the link provided below for details regarding a course in M.Arch from Sushant School of Art and Architecture. You can download their brochure which contains important details like eligibility, application dates, fee structures and contact information.
https://www.shiksha.com/architecture-planning/interior-design/course/m-arch-in-interior-architecture-sushant-school-of-art-and-architecture-ansal-university-gurgaon-276305

For fee details, you will have to directly get in touch with the college officials. Sharing the link to get the contact details of the college.
Link: https://www.dreamzone.co.in/

Hello, Central Saint Martins in London where Stella McCartney, John Galliano and Alexander McQueen once studied tops the chart. Parsons, at The New School for Design in New York, is third. Toronto's George Brown College is tops in Canada at 24th on the list. Ryerson University, also in Toronto, isn't far behind at 26th.
Good luck.
Thank you.

Please check the link in which you will find the names of institute along with a great article on designing:
https://www.shiksha.com/design/industrial-product-design/articles/top-10-design-institutes-in-india-blogId-8287

Please refer to the link provided below for details regarding cut-offs for students in the reserved category to gain admission into NID.
https://www.shiksha.com/design/fashion-design/articles/nid-admissions-2016-cut-off-scores-blogId-12369

There is no standard 'International exam' for fashion designing. You need to apply for each school separately. Schools usually require an essay and portfolio. This process starts in November itself.

NIFT offers master in fashion management which might be what you're looking for. Heres a link to check that out- http://www.nift.ac.in/mfm.

To apply for MFM you need to have UG degree in any discipline from any Institute / University recognized by law in India or an undergraduate Diploma of minimum three years duration from NIFT / NID. There is no particular cut off announced by the college.