What are the normal noises?

There are quite a few on the Prius, but the first one that I really noticed (other than silence at the redlights ), was a electric motor run sound that starts (not always, but frequently) a few seconds after you shut the Prius off. This is a electrically powered pump that circulates hot engine coolant into what is basically a 2-3 liter capacity thermos bottle which helps bring the engine up to temperature faster when you next start.

As I recall, the 2010's onward use another method to heat the engine more quickly rather than the pump and thermos storage bottle.

 

The Prius inverter runs whenever the car is READY, and will emit a constant whine. Open the hood and put your ear next to the inverter (it has a shiny aluminum cover) to hear it.

To force the brake pressure accumulator pump to run, make the car READY, then depress the brake pedal repeatedly. The pump will run from time to time to restore hydraulic pressure in the brake system.

If some rust has built up on the front discs then the brakes may make some noise. You might try cleaning the brakes by getting up to 50 mph or so on a road with no traffic behind you. Then shift to N, and moderately brake to a stop. Repeat a few times. The idea of shifting to N is to force only friction braking to operate, so that the discs can be cleaned by the brake pads.

If the rear brakes are making noise, then the brake drums have to be removed and brake parts cleaner used to clean the brake drums and shoes.

 

The point of forcing the pump to run is to become familiar with the sound that it makes, so that you recognize this as one of the "normal" sounds produced by the Prius.

You'll have to decide whether the squeaking sound is produced by the brakes or the suspension. If these sounds can be demonstrated, maybe you should take your car to your local dealer for assistance.

 

Well, you can either record the sound and post; or else you can find another Prius to drive and see how the pump on that car sounds, compared to your vehicle.

 

Thanks for the update.

It is too early to say whether you need to find a new dealer for in-warranty service. See what happens with the brake pressure accumulator pump replacement. That is a fairly complex job and would cost you ~$2K out of warranty. If the job is done well, then no reason to change.

When you pick up your car, you can stop at the parts counter and buy 4 qt of Toyota ATF WS and two aluminum washers for the drain and fill plugs. That will set you back around $40.

Then fabricate a suitable funnel with a 3 ft. long tail, buy a 24 mm socket and 10 mm hex key socket, and a couple of jackstands to lift up the front of the car, and you will be good to go.

I note that your car is a 2009. I don't think that you need to change the transaxle ATF until 30K miles have been logged, unless you really want to baby your car.