The fan motor on our nonvented propane fireplace has a high pitched hum regardless of the rpm's... what is causing this?

If this has just started then the noise could be caused by lack of lubrication. Most small fans like the one you have do not have oil holes to put the lubricant in. Sometimes you can get around this by placing some lubricant in or around the shaft areas on both the front and back sides of the motor shaft. If not then if the fan motor is causing this noise it will need to be replaced if it is that bothersome.

Now it could also be dirt on the fan blade or cage wheel that spins around. This can be taken apart and cleaned to see if that solves the problem. There are a few other reasons but those get technical in nature and you would have no way to rebalance the assembly any way. In fact most repair persons do not do a rebalance but just replace the subject assembly.