The petty offense may not disqualify you from DAPA but I suggest that you wait for further guidance and the federal regulations to be issued in early 2015.
Everything depends on whether the court disposition pushes the case into the "significant misdemeanor" category. You may still be ok. Impossible to say here.
It depends. One would need to read the language of the CA penal code under which you were convicted to understand whether your particular conviction will be considered a "significant misdemeanor", in which case you will not be eligible for DAPA. I personally don't think a simple petty theft elevates you to that nasty level, but you never know for sure until analyze the conviction section.
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