Can I work with legally void EAD while Green Card application is processing ?

Hi, here is my situation. I currently hold an EAD valid from 6/01 to 5/31. I don't have a job yet and am running on the 90 days of unemployment allowed (ending 8/31). I got married on May 16 and am about to file my GC application. My questions are: - if I don't have a job by Aug. 31, my EAD is void. But can I still look for a job based on my pending GC application, or do I have to ask for a new EAD with my GC application package even though the current EAD is still valid (until Aug. 31) ? - if I find a job before Aug. 31, do I have to ask for another EAD with my GC, or is my current EAD based on student OPT valid until receipt of GC ? Thanks for your help.