Your car is leaking yellow rusty water Does a radiator leak normally give out that type of water?
Yes, this sounds like coolant from a cooling system that has been neglected and not flushed and changed regularly. Have the leak fixed, a new thermostat installed, a fresh mix of 50/50 coolant installed, and bleed the system.
Number one, replace the water pumb. Usually when water leaks from the pump it is through what is called a seep hole and signifies the pump is bad. That brown fluid is probably water with alot of rust mixed in it. Good idea to have the radiator flushed and filled with new coolant. rusty water, change the water pump