No heat with slight waterworks

My 2003 Dodge Stratus has been overheating whenever I turn the heater on. The heater itself, up till this started, slowly flickered from cold to short bursts of hot then just blew cold. There is a thick black tube that runs just a few inches from the overflow tank to connect to the top of a black part that has four bolts securing a cover from which sprays all the fluid running out of the tank. What might this part be and to what system of the car’s function does this part actually belong?

Go to your mechanic IMMEDIATELY. Continuing to drive this car with coolant leaking like this will DESTROY THE ENGINE!!! Since you cannot tell me the names of the parts that are leaking, I cannot tell you how to stop the leak other than letting a qualified mechanic fix this for you correctly. This is a serious, and the fix may not be.

A good place to start would be replacing the thermostat. As BustedKnuckles said though, driving the car while the temp gauge is in the red will quickly damage your engine.