It really sounds like something is going on with your blower motor. If the blower motor runs, it wouldn't make sense the blower fuse as a problem. The fuse is a strip fuse. The little fuse case is by the left (drivers side) shock/strut tower under the hood. It's black plastic and the top of it you squeeze a little and it flips to one side, you'll see one wire on each side of the black box, has a couple phillips screws holding it in place.
See if the whirring noise on startup goes away if you push the "O" button before starting the car, I'm still kind of thinking the blower motor is the problem and is noisy when first started, seen this complaint before.
Lets see, what else did you want to know:
The debris hitting the innards of the waterpump making a noise-possible, never ever heard of it before and I severly doubt it, but possible I suppose. Sure wouldn't think a noise like this would be described as "whirring" either.
If the heater core were blocked by debris inside the cooling system, it would only affect the flow of coolant throught the core tubes, not the core fins, which is where the air flows through. So, no, by your line of reasoning, debris in the cooling system by the head gasket job, it would not affect the fan or amount of airflow to the cabin, but could affect the temp of the air by plugging the core tubes only. If the heater core fins became plugged somehow, like by a heavy dust accumulation, it could hinder the airflow, but I've never heard of this. I've heard of evaporator cores plugging up due to freon leaks causing an accumulation of refrigerant oil and then collecting dust and clogging the fins, this is all a different topic though. Also the evaporator can ice up for various reasons and stop airflow, this happens usually in the summertime due to high humidity levels.
Based on all the info I have, I would say the most likely cause for the problem is a bad blower motor, possibly too much axial play in the motor shaft allowing one of the fans to hit the blower case.
The fan is buried under the wiper assembly. It has a central motor with a "squirrel cage" type fan on each side of the motor, running on a common shaft.
Where is "western Michigan"? When I think about it, I guess you could consider the U.P. as "western" Michigan as well, or are you in the lower peninsula on the western side? (just curious, I love the U.P.)
If you push down the "O" button, it should stay down and shut off the system, you shouldn't have to hold it down manually. Sounds like probably the problem is a mechanical defect in the push button panel.