Design Entrance Exam

NIFT does not offer 6 months masters course.

As per NIFT's prospectus, the eligibility for MFM (Master of Fashion Management) is :
An Undergraduate Degree from any Institute / University recognized by law in India.
or
An Undergraduate Diploma of minimum three years duration from NIFT / NID.
So you cannot sit for the exam until or unless you have the certificate.

You will have to appear for entrance exam conducted by NIFT.

Yes, you can apply for the same. But, you will have to appear for the entrance exam and clear it to get yourself enrolled.

Yes, after completing FCT from NIFT, you will get ample of career options to go for.

Yes, you can. You will have to appear in Design Aptitude Test which is meant for admission in NID. Since, you are a class 12th student, you can appear in it which is scheduled in the month of January next year (2018). I would like to tell you that 31st October 2017 is the last date to apply, so you should hurry up.

It is the common exam for entrance for Maters Design program in any of the IITs.

The best things to do is refer to question papers from the previous years and get yourself to start thinking in that direction. Time yourself and get in the habit of finishing all the questions in the given time. You can refer to books by Arihant or honestly, any publication. With CAT, you need to focus more on your drawing skills. An innovative idea is important but your drawing skills will help you communicate that idea to the examiner. Good drawing skills make a world of examination. For GAT, you need to basic class 10th knowledge for logic, English and maths. For GK, you need to go through the news every single day.

Please refer to the link mentioned below:
http://www.nift.ac.in/kolkata/ce_cpt.html