If you want to attend both the modules in June 2013, there should be a gap of 9 months from the time of registration. Last date will be 31.08.2012.
You will be eligible to write a single module in June 2013 if you enroll after August 31st but before 30.11.2012. 6 months gap.
You can check the below link :
And also write to the email ID basing on your region from the below link:
General Queries :info @ icsi.edu
CS Brouchure for more information:
2) to answer your second question there is no cutoff marks specified for Bcom.