Its a Forester oil cooler from an automatic. Standard Subaru equipment. The copper heat exchanger goes for about $300 by itself. Teagues Auto sells a kit.
The hose is Aeroquip AQP hose. Rated for oil, gas, coolant - reinforced by an internal nylon braid. Stainless steel braid would just abraid away at the cross member and the engine block like a file.
The red fitting is a 120 degree 8AN fitting. A 90 degree fitting will not work.
Here is a closeup of the copper heat exchanger and the coolant return bung.