What is a heater coil and a heater core?
The heater coil and a heater core is the same thing. Hot water circulates from the engine and through the heater core then back to engine generating heat for your heater system.
Which hose gets cut and spliced back together on a 1998 Lincoln Navigator to bypass the front heater coil?
Sounds like heater core is leaking and needs to be replaced You probably have a leak in the heater coil of the air conditioning system. You can either get the coolant flow to the heater coil shut off (cheapest) and get along without heat in the car, get the heater coil repaired (iffy), or get it replaced (maybe get a used part from an auto salvage yard.
If you are talking about a heater core it is usally behind the glove compartment or in that general area. You need to disconect the heater hoses from the engine compartment and pull out the core. Every model is slightly different in the way you reach the heater core. You need to get a repair manual at any auto parts store. They only cost about $15 or try e-bay for a better price.
Second time on replacing your 1995 Sunfire heater coil Anyone have this problem or know of a recall for this problem?
Heater coil? Or do you mean the heater core? If it's the core, the problem might be due to rust in the cooling system. This is usually because someone just filled or topped off the system with plain water instead of a 50/50 mix of water/antifreeze. I'd have the whole cooling system flushed before replacing another heater core, and make sure the proper mix of water/antifreeze is used to refill the system.