Can a 16-year-old who suffers from emotional abuse runaway legally as long as he's in a suitable living environment?

There is not such an act as "legally running away". A minor is presumed by law to be under the physical custody of his or her parents or legal guardian until he or she reaches the age of majority or until a court rules otherwise. The law does not recognize emotional or mental abuse as such unless it is documented by the state agency authorized to oversee the welfare of minor children.