Degree

Hello! https://iimcat.ac.in/per/g01/pub/756/ASM/WebPortal/1/index.html?756@1@1#!
Kindly visit this link and check the "registration" section under FAQs about the eligibility criteria of the CAT exam.

Since ICWA degree is equivalent to graduation, most probably you are eligible to take admission. But still, you can confirm it by contacting the institute or physically visit the institute.
If you are a working person and want to enhance job value, position in your organisation and in your career, surely it is appropriate.

Yes, you can take admission in Bachelors degree after 12th.

Hello Akash,
Some universities do accept engineering as the eligibility for admission to M.Sc courses. If your intended institute is accepting it then you can go ahead. But I would advise you to go for executive MBA of one year in one of the IIMs.

Yes, you can because you are a graduate now.

Do you mean that you will study in India and look for a job in the US or study any of these in the US and work there? Whatever you mean, my recommendation goes for an MBA from a reputed university if you are interested in Business. If not, then first find out what you wish to do and go for it. All streams/courses have ample scope in the US or India.