New Way Forward Act This bill makes changes to immigration enforcement, including ending mandatory detention in certain cases. The Department of Homeland Security (DHS) shall not enter into or extend any contract with any public or private for-profit entity to own or operate a facility to detain aliens in DHS custody. The bill provides for various protections related to detaining aliens, such as (1) requiring DHS to make an initial custody determination and establish probable cause within 48 hours of taking an alien into custody, (2) establishing in hearings related to such determinations a presumption that the alien be released, and (3) requiring immigration judges to impose the least restrictive detention conditions necessary. A DHS officer may not interrogate a person as to immigration status based on factors such as the person's race, religion, sexual orientation, or spoken language. The bill removes mandatory detention requirements for certain aliens, such as asylum seekers with a credible fear of persecution. Removal proceedings against certain aliens previously admitted into the United States must commence within five years of the alien becoming deportable or inadmissible. The bill also removes certain crime-related grounds of inadmissibility and deportability. The bill gives immigration judges discretion to provide relief from removal if the removal is not based on certain crime-related grounds. State or local officers are prohibited from performing certain immigration enforcement functions, such as apprehending aliens. The National Crime Information Center database shall not contain an alien's immigration information. The bill repeals provisions providing criminal penalties for improper entry or reentry into the United States.