Colleges in Gangtok

It is always better to do hotel management from an IHM. They are well known in the hospitality circles for the quality professionals they produce. Almost all IHMs gives the students, really good placement options. But salary wise expect a starting salary (management trainee) between INR. 1.5 Lacs - INR. 4 Lacs CTC per annum.

According to last year cutoff, there is very less chance as last year cutoff was 9K around.

Your options would be:
IHM Gurdaspur
IHM Guwahati
IHM Shillong
IHM Srinagar
IHM Hajipu

If you're a general category student then no, there is no chance, but if you're a SC/ST/OBC category student then maybe you'll get a state government IHM.

No, you can't get this college as per your rank. For more details, visit this link:
https://nchmcounselling.nic.in/NCHMRegistration/report/OpenCloseRank.aspx?boardId=1003

IHM entrance exam taken by NCHMCT JEE

Yes, you can apply for sure. The only thing is that you have to give your Gate or respective entrance if any college conduct in CS. I have seen many of my friends getting a good rank irrespective of the branch they come from. I am talking about CSE branch though.
All the best.

If you are from general category, you need to have a rank between 15-400 for best College that includes IHM Pusa, Bangalore and Mumbai. If you are from OBC, you can have rank till 1800 for Pusa 5000 for Mumbai 9000 for Bangalore.