AFG and SAFER Program Reauthorization Act of 2017 This bill amends the the Federal Fire Prevention and Control Act of 1974 to: (1) repeal the expiration dates of, and to reauthorize through FY2023, the Assistance to Firefighters Grants (AFG) Program, the Fire Prevention and Safety Grants (FPSG) Program, and the Staffing for Adequate Fire and Emergency Response Grant (SAFER) Program; and (2) authorize the use of AFG Program grants, instead of SAFER Program grants, to provide specialized training to first responders on how to recognize and properly intervene with individuals with mental illness. The SAFER Program is revised to permit the use of grants to change the status of part-time or paid-on-call firefighters to full-time firefighters. The United States Fire Administration (USFA) may develop and make widely available an electronic, online training course for members of the fire and emergency response community on matters related to the administration of AFG, FPSG, and SAFER grants. The Federal Emergency Management Agency (FEMA) shall ensure that any such training is: (1) tailored to the financial and time constraints of members of the fire and emergency response community; and (2) accessible to all individuals in the career, combination, paid-on-call, and volunteer fire and emergency response community. The USFA shall develop and implement a grant monitoring and oversight framework to mitigate and minimize risks of fraud, waste, abuse, and mismanagement relating to such grants programs.