Northern Triangle and Border Stabilization Act This bill authorizes assistance to the Northern Triangle countries (El Salvador, Guatemala, and Honduras) to address the causes of migration to the United States and contains provisions related to the handling of such migrants. The Department of State shall create and implement a Northern Triangle strategy to (1) address crime and violence, (2) improve democratic governance, and (3) promote economic development and tackle extreme poverty. The State Department shall (1) help strengthen the capacity of Western Hemisphere countries to accept and care for refugees, and (2) establish Designated Processing Centers in various Latin American countries to process individuals seeking to migrate to the United States. At least 100,000 additional nationals from Northern Triangle countries shall be admitted as refugees each year from FY2020 through FY2024. The bill requires the hiring of additional Customs and Border Protection (CBP) officers, immigration judges, and related staff. The Department of Homeland Security shall establish standards of minimum care for individuals in CBP custody and additional guidelines and standards relating to children in CBP custody. The bill expands penalties related to smuggling and establishes criminal penalties for certain actions related to evading border controls. The bill contains various other immigration-related provisions, including (1) limits on when asylum applicants may be removed, (2) an expansion of alternatives to detention programs, and (3) a requirement that the Department of Justice provide counsel to children and particularly vulnerable individuals in immigration proceedings.