You must answer all questions truthfully. USCIS may investigate the circumstances of your adjustment application again and you may lose your resident status. You may be better off if you do not apply for citizenship. I recommend consulting with an immigration attorney.
It appears that he was deported twice. This may bar him permanently under the current law and he would have to reside outside the US for 10 years first before he becomes eligible for a waiver.
You should consult with an immigration attorney for a review of his case.
Your DUI should not prevent you from becoming a permanent resident but your unlawful entry will be an issue. You should consult with an immigration attorney before you submit any applications to USCIS.