Engine overheating 92 ford escort , over heats , weve replaced , head , radiator, thermostat,bypassed heater core, all fluids are fresh and clean no discolor. did not change water pump though , could it not be working properly. does it need to be replaced even though it does not leak .

Couple of thoughts. are you losing water/antifreeze, do you have the right mixture 50/50 water/antifreeze. You did not say if the thermostat is removed or replaced. If thermostat is stuck closed water will no circulate. Are you getting any flow from the water pump. If your heater core is bypassed you should not get any hot air from the heater in the vehicle. Make sure your oil levels are good.
https://www.dummies.com/home-garden/car-repair/heating-cooling-system/how-to-troubleshoot-an-overheating-engine/
https://www.thoughtco.com/figure-out-why-your-car-is-overheating-281320

Yes you bypassed the heater core which is the radiator that supplies the heat for the passenger compartment

No a heater core alone will not cause a vehicle to overheat. The heater cores sole purpose is to transfer heat generated by the engine to the blower motor so that you can get heat from your car vents. A person could technically remove the heater core from the vehicle and connect the hoses together to bypass it, and the car will run as if nothing happened, minus the lack of heat in the vents.

If the car is overheating, there are three mai issues that could be happening. 1) The radiator is blocked and not allowing coolant to be cooled off before returning to the engine.
2) The water pump is broken. The engine relies on this pump to move the coolant throughout the engine. It may not leak as long as the gasket is alright but the impeller ( small fans on the inside of the water pump ) could not be turning.
3) Lastly and most commonly is a faulty Thermostat. The thermostat is the valve which opens and closes at certain tempuratures and decides if hot coolant stays in the engine or circulates to the radiator to be cooled off. If the thermostat fails, unless you have a failsafe one, will fail in the closed position keeping the hot coolant in the engine and causing it to overheat.

The thermostat is by far the cheapest of the issues so consider changing that first along with a coolant flush before considering putting a new rad or waterpump. You can usually get a thermostat, 2 jugs of coolant and a flush kit for about 50$ at pretty much any parts store. Becareful however not to drive a overheating vehicle as gasket burning and head warpage can occur, which will require rebuilding th head.

Good Luck

Do the electric cooling fans turn on ?

YOU NEED TO FLUSH THE RADIATOR AND CYLINDER BLOCK AND HEATER CORE.CHECK ENGINE OIL IN CRANK CASE IF LOOKS LIKE MILK SHAKE YOU HAVE A BLOWN HEAD GASKET.WHICH WILL CAUSE ENGINE TO OVER HEAT.

it appears that you have a large air pocket/low on coolant. The engine is getting hot due to the lack of coolant but there is no heat because nothing is flowing through the core.

No, you just won't have water flow through the heater core, Coolant flows through the engine through the lower radiator hose as the water pump sucks it out of the radiator and pushes it through the engine. It then flows out the top radiator hose when the thermostat opens. It then flows into the radiator to cool off.

Is your heater core leaking?

Sounds like to me it would be your water pump before a heater core. When the water pump goes out, it stops pumping the coolant through the system which is what would cause it to still overheat even with the thermostat out. Change the water pump and you should be good. Let me know if you have any other questions. Thanks for using FixYa!

No water pump issues I am aware off, are you sure you bled the air out of the cooling system? If not fill the overflow bottle all the way full, then use a floor jack and raise the front of the car as high as you can ( this allows air to go to top of radiator tank), then run the engine at high idle speed until the cooling fan ( I assume the fan works OK?) comes on, but avoid letting the engine get into the overheat area of the guage, if it does turn it off, run water over the radiator until it cools, check the tank and radiator, top off if you need to and repeat above procedure, if this doesn't work you have some other problem like no or little flow in radiator.