The heater and noises!

Turn off heater/air conditioner and accelerate briskly. If noise does not occur problem is probably a regulator in the heater/air conditioning system located under the dash.

DO YOU MEAN HEATER CORE if so it is in the havac box under the dash

I've never heard of "burping" the coolant system, nor have I ever owned a Lincoln, but based on your description of the problem alone, I would first drain the system, flush it with a good radiator flush (ask the guys at a reputable auto parts store) and refill it - checking all hoses first, of course. While you're at it you might want to check out the water pump and thermostat. The other thing is that the sound you describe as water rush may not be that at all - although i have no suggestions as to what it is. Good luck. . .

JB

It sounds like a vacuum line is leaking or broke. Check the lines under the hood and dash.

it could be in fact the turn signal sound since this is produced electronically by the cluster

pull the cluster and confirm its making the sound

I replaced quite a few at the dealer for similar concerns

The dash will have to be removed to access the heater box for removal.I would suggest that if you've never done this to have a repair shop do it for you.Its not easy even for a experienced mechanic.

Sounds like the heater and a/c blend door actuator. It is located under front center of dash below windshield. Dash must be removed to replace it. I've done it several times.

wheel speed sensor. check with your dealer on cost and availability

try resetting the fuel pump inertia switch located in the side of the trunk.

The heater and a/c blend door actuator motor is located behind the center of the dash just below the windshield. The steering column must be detached and lowered and the dash must be removed to access the blend door motor.