Class 11

Class 11th standard result is not so important. It is just like a practice test for class 12th.

You can apply it after 12th. Yes, you can pursue hotel management or be eligible for NCHMCT-JEE if your steam is arts. It is just that, you need to start preparing for the exams. Better results in the entrance exams will give you better college.

Yes, you can apply for NCHMCT JEE 2018.

Students from class 11th will not be allowed to appear for the NEET UG examination.
Students who will be appearing in class 12 board examinations or whose result is awaited are eligible to appear for NEET 2018.
NEET Eligibility Criteria 2018 - age criteria
According to the NEET 2018 eligibility criteria, a candidate has to complete 17 years of age either at the time of admissions or else on or before December 31, 2018. Hope this helps. Regards.

You could select a course of your choice in class 11, and pursue computer Science and graphic design on the side, till you have the option to pursue higher studies later on in your career. Please refer to the link provided below for careers after class 12. If you are confused about which stream you should pursue, you should do an in-depth analysis of your options. You can pursue computer Science in class 11 but for that you will have to opt for the Science stream. The choice is yours.
https://www.shiksha.com/careers