the two heater pipes should be sticking thru the firewall, and yes outer would be towards the outside of the car. I'd expect the heater control valve to leak once you hook it up
Once you've determined that the core does not leak, I would check the control valve for functionality....even if it does not leak.
Besides leaking, those valves are prone to sticking, or reduced movement. These conditions cause the heat to be on all the time. Prolly why the core was disconnected to begin with.