A peripatetic is someone who likes to wander around or constantly travel, a nomad in other words.
When Benson is voicing her frustration over what to do with Sophie/Grace, Carisi suggests she could be "5150'ed." Section 5150 of the California Welfare and Institutions Code allows peace officers to detain the mentally ill for medical evaluation. This statute has no effect outside of California, and certainly not in New York City, where SVU is set. New York officers have a mental hygiene statute, Section 9.41, but they would likely reference it as "mental hygiene" or an "emergency committal."