CAT

The dates for CAT are still not out. The exam generally happens in late November though.

There is no specific required time for preparation. It depends from person to person and his/her ability to grasp concepts.
For majority students, I'd recommend joining a one year program at a proper coaching center. It typically starts around August, September and coaches you till the exam next year.
Make sure that you give all their mock tests and analyze the results as well (where you went right, where you went wrong). That always help you find your strengths and weaknesses and thus tackle your main exam accordingly.

No. Calculator is not allowed in the CAT exam. However, you get an on-screen calculator that you can use. Having said that, CAT questions are generally framed in a way where you won't really required using a calculator.

yes any graduate can appear for CAT /MAT.

I don't think that you will be able to fill in the CAT form as you do not meet the minimum criteria of 50%. Please have a look at the eligibility criteria for appearing in CAT examination.

You may refer to following link for tips on cracking CAT: https://www.shiksha.com/mba/exams/cat/preparation-tips

No, it will not hamper your admission. Prepare well for the GD-PI-WAT round. Be prepared for justifying the reason for the break in a well-versed manner and all shall be well! All the best!

It is once in a year.

Your grade 12th marks will effect your acceptance a little. You should be able to prove that you are more than your grade 12 marks by your skills and knowledge in the interview. Before all that, you need to perform exceedingly well in your CAT to get an interview call.

Every year, IIMs announce their CAT marking scheme. Marking scheme announced for CAT 2016 had 3 marks for every correct answer and 1 mark deducted from your credit score for every wrong answer. The exception is Non-MCQs where your wrong answers will not impose penalty ofnegative marking.