He can face both. he can be deported simply for being here without lawful status. whether he is convicted in criminal court or not. You should speak with attorneys well versed in criminal and immigration law.
If the cases were all dismissed they should not be held against you, since they are not convictions. You may want to bring all of the court paperwork to an attorney to review and confirm that the cases were resolved in the fashion you believe.
You may be able to expunge the DUI bit it will be meaningless in the immigration context since you must disclose all convictions. The conviction should not prevent you from getting the H1B visa, though.
Petition for your wife and child now. The wait is about 2 years and 4 months as of the current visa bulletin. If you decide to naturalize, there is no waiting time, but you do not say when you would be eligible to apply for naturalization.