There is absolutely NO NEED for you guys to be doing your own background checks UNLESS You have been charged or convicted of a crime.

When you apply for the relief of Deferred action you will be given an appointment for biometrics from the USCIS which is when you have your picture take and finger prints, which are use to check your background.

Even if you have been convicted of a crime you should be getting your certified disposition of the case the background check will be done by USCIS.