What is going on with my water pump?

Are you asking if coolant is coming out from a leaky gasket and the hole in the assembly meaning the bearing is shot? Time for a replacement no matter where it is leaking.

No it's pumping out the inlet and outlet both on the water pump. Now with a new water pump, thermostat, heads, timing chain kit and all new gaskets it's overheating. Watching temp gauge and thermostat is working.

Also bled air out of it.

I'm assuming you have the 5.9L V8. The small hose connection is for the heater core. It's also an output connection. When the engine is cold and the thermostat is closed coolant is pumped directly to the heater core so you have heat in the passenger's compartment faster. Hope that helps! Jim