Fairly Assessing Service-related Toxic Exposure Residuals Presumptions Act or the FASTER Presumptions Act This bill revises policies and procedures of the Department of Veterans Affairs (VA) related to establishing or modifying presumptions of service-connection based on toxic exposure. The bill sets up a procedure by which the VA must determine whether to establish, remove, or modify via regulations presumptions of service-connection based on toxic exposure. Specifically, the bill establishes within the VA the Formal Advisory Committee on Toxic Exposure, the Science Review Board, and the Working Group to assist with the various procedures in establishing or removing presumptions of service-connection. Such procedures include assessing the exposure of veterans to toxic substances during active service, evaluating research on the health effects of exposure, and making recommendations based on the evidence and research. The bill also establishes the Expert Advisory Panel on Constrictive Bronchiolitis within the VA to develop guidelines for VA research on symptomatic veterans who served on active duty in the Southwest Asia theater of operations and have bronchiolitis. The Department of Defense must develop and implement a plan to strengthen data collection with respect to members of the Armed Forces (including the reserve components) who are exposed to toxic substances while serving. The VA must initiate or sponsor various studies related to veterans who served on active duty in certain locations. Finally, the VA must provide annual training to relevant employees to improve the handling of claims for compensation and benefits that relate to toxic exposure.