CUSAT

Go for NCHMCT because it is a national level exam basically for admission in 21 central universities of hotel management. I will suggest you to opt for this and score good marks so that you can confirm your seat in one of the government college. For any other query please feel free to ask.
https://www.google.co.in/amp/s/www.shiksha.com/hospitality-travel/hotel-hospitality-management/exams/amp/nchmct-jee

All the courses offered by CUSAT has their own entrance tests except MBA. For MBA, any of the exams like CAT CMAT or KMAT is accepted. The CAT exam conducted for other courses by CUSAT is not applicable for any other universities.

The time for applying is over. If you have already applied, please check the website to see your schedule of GD&PI to know if you are selected or not.

The list is already out. Please check the website.

The classes will be starting from June or July.

SMS-CUSAT doesn't accept MAT scores. You must have CAT/CMAT/KMAT scores.

Yes, the last date was 8th March, 2018.

CUSAT CAT Question & Sample Papers 2018 are available at the link provided below:
https://www.shiksha.com/university/cochin-university-of-science-and-technology/exams/cusat-cat/question-papers.