Yes, it is necessary to apply to before the CAT results are out. You must have applied to IIMs while filling the CAT application form. For other bschools you have to apply before the results are out. Yo ushould go and visit the websites of colleges you want to apply to and check the deadlines. Usually most colleges have deadlines before the CAT result gets out. You must have an idea of how much you can score. Check the criteria for different bschools online and apply to them. Once the deadline is over they do not open after CAT results. 

Yes, it's recommended to apply to some of the colleges of your interest which you think are decent enough for you to study. With your past performance, you might have some idea regarding what your percentile might be.
For more details you can refer to
https://www.google.co.in/amp/s/bschool.careers360.com/articles/cat-percentile-predictor%3famp#ampshare=https://bschool.careers360.com/articles/cat-percentile-predictor. 
The above link also has score predictor, you can check via that. Other than that yes, few colleges might reopen their application forms again.
All the best!!

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