Fairness for Immigrant Families Act This bill modifies provisions barring certain aliens from admission and addresses other immigration-related issues. The bill repeals various admissions bars against aliens who were unlawfully present in the United States for certain amounts of time. The bill also modifies a provision that generally makes inadmissible aliens who had been ordered removed and who attempt to reenter the United States without being admitted. Specifically, the bill exempts from that provision minors, asylum seekers, aliens who received a stay of removal under a family unity program, victims of severe trafficking, and certain aliens who entered the United States as children. An alien who entered the United States without inspection may apply for lawful permanent residence during the five-year period starting from this bill's enactment if the alien is the beneficiary of a family-based petition or labor certification. The bill also prohibits removing an alien with certain pending immigration-related applications, such as an application for a family-based immigrant visa, if the application is not obviously deficient. Before removing a parent or legal guardian of an individual who is less than 21 years old and a U.S. citizen or permanent resident, the Director of U.S. Immigration and Customs Enforcement must review and approve the removal. Furthermore, the bill makes it a crime to fraudulently provide immigration services. The Department of Justice must make grants to support enforcement of such laws and to assist victims. The bill establishes the National Office of New Americans to support the integration of immigrants and refugees.