The heater (fan) makes a loud noise.

That sounds terminal, it sounds like they forgot to fill with oil. Your big end bearing are shot.

The only time i have encountered this problem it turned out to be a cracked fan wheel in the blower. fooled me until the fanwheel disengrated and locked up the blower motor.. could be trash in the blower too like leaves, plastic bag etc.

If the engine is not reaching optimum operating temperature it will indeed give you a "check engine light",the code will lean you in that direction as well.The noise your hearing more than likely is coming from the "clutch fan",they are very common on the TrailBlazers to make noise and fail.The oil light... you certainly need to have the oil pressure checked with a mechanical gage.

change the blower motor

This noise can be caused by a defective outboard (wheel end) front axle constant velocity joint (known as a "CV" Joint). This would be louder on turns, more noticeable at lower speeds and sharp turns. Next it could be valve train noise, this would come from the top of the engine and this could be related to the oil change if a piece of dirt got into the oil supply to the hydraulic camshaft followers. At this point you need a professional to listen to the noise to determine the exact cause.

Possible. If you have changed tires lately, make sure they put the right size tires on. If they went up in size by any measure, it could be rubbing on the tire well and thus making the noise. Check the users manual if you have it and check to make sure the tire sizes are correct. Also check your power steering fluid. That would make a humming or moaning noise but it would be noticeable while turning.

change the relay and fan motor together.

The fan is rubbing ,was any of you srews striped, if they are replace with some larger screws and that will realiagn the motor

yes your right... it could be the wheel bearings, try replacing them.

Your heater fan bearing is shot,,time to replace Fan now before you really need it.