Well if you can take coaching then You should Go because you will be able to compete with your batchmates and will know the real Problems of the exam before the exam, But there are many students who clear CAT without coaching so again if you have good planning and self-discipline and you are able to stick to the deadlines then You can prepare for Yourself.

If you are preparing Yourself then don't forget to make progress report where you are going to mention what You have read each day and how much Problems did you solved every day to keep track of Your speed and You will be able to determine that How much time you should spend on each topic you score well in the exam.

It depends on your capability. There are many students who prefer CAT preparation by self but it is recommended that if you are unable to prepare by self definitely choose to take up professional guidance.
The time is less to prepare for the exam and you will have to speeden up with the preparation and then the revision.
Read a newspaper online daily. It can done in your spare time. It could be The Hindu or Firstpost.
Also start Word Power Made Easy by Norman Lewis.
Refer to detailed correspondence material online like of TIME or some other good brand.
Refer to previous year papers, practice them, attempt them again and get good in the sections.
Once you know which section you are good in and in which you are weak, focus on weak sections and do not escape.
Time is less so do not spend much time on one.
Give sectional online/offline mocks and analyse your preparation.


Good Luck!