Protecting Families and Improving Immigration Procedures Act This bill establishes limitations on separating alien children from parents and on detaining families, and also addresses other immigration-related matters. A child may be separated from a parent or legal guardian at or near a port of entry or U.S. border only if (1) a state court has made a relevant ruling, such as terminating the parent's rights; (2) a qualified child welfare agency official has ruled that separation is in the child's best interest; or (3) a specified official makes certain determinations, such as concluding that a child is a trafficking victim. A child may not be separated from a parent or guardian solely to deter migration or promote compliance with immigration laws. This bill establishes presumptions (1) in favor of family unity and keeping siblings together, and (2) against detention. The Department of Homeland Security (DHS) shall (1) document all child separations, (2) develop training for officers handling separations, (3) publish guidance on how to locate a separated child, (4) periodically provide a parent or guardian information about a separated child, and (5) pay for counsel to represent unaccompanied alien children in removal proceedings. The Flores settlement (an agreement imposing conditions on the treatment of detained alien minors) and a related court holding shall apply to the detention of families. The Department of Justice shall increase the number of immigration judges and support staff. Immigration judges may suspend removal proceedings in certain instances, such as when the alien appears to be prima facie eligible for another immigration benefit.