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ANSWER: Unfortunately, I do not have very good news. Since 2012, the USCIS has been strictly enforcing the rule that the OPT request must be filed within 30 days of the DSO certifying the I-20.
You can find this information here: http://www.cilawgroup.com/news/2012/11/01/uscis-now-stringently-enforcing-filing-deadlines-for-student-i-765-opt-applications/
As far as working, you cannot be employed unless you have a valid EAD in hand and the employment is commensurate with that valid EAD.
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