New 2005 Prius Owner!!!! Have a few questions.......

The spoiler rattle is not normal. It needs tightening. Tell the dealer.

Driving such short distances is not the best use of the Prius. It may not have been the best choice for this use. Are you sure the tank was full at the beginning of the 120 miles? It could read full and still have used a couple of gallons and that could be nearly 100 miles difference.

No, I don't think there is a way to make the radio readout stay up. Wish there was.

Sounds after turning off the system are normal. It is part of the system efficiency.

Congrats and enjoy. Sounds like you got a good deal.

 

Rear Spoiler coming loose | PriusChat
How to remove/replace spoiler | PriusChat

I think I would take it back and ask them to do it unless you just enjoy this kind of thing.

It's not impossible the tank meter is wrong. Accuracy is not it's strong point. The other possibility to the low MPG is a weak 12V that causes the engine to run more than it should. A low 12V causes many strange issues. Try this onboard test. Weird stuff happening? MPGs dropping? Test The Battery | PriusChat
Report all 3 values back here.

 

I have an '05 for comparison

Rattle- since its an hour away if u r mechanically inclined u can pop the black plastic cover off the back of the hatch and try to tighten the bolts from there. It might just b that one of the nuts dropped off.

My mpg matches - computer vs pump.

In 1st 5 minutes of running best milage i get is 45, but normally its 30-35. This is due to the engine running to warm up the drive system. There appears to b no way around this.

I get 48 mpg highway and 56 mixed hwy/cty. I drive 35 minutes 1 way for reference.

 

Yes you can get the radio screen.

Press the "Audio" button on the left side of the MFD(multi function display) when the car is power on(ready). Choose your audio choice, Radio, CD, cassette.. Press the info button on the right side of the steering wheel will resume to show hybrid information. Also after shut down and power on, the MFD will show hybrid information again(default). Press '"Audio" again every time when you like to see the radio screen.

 

Are you calculating your mileage using the gas gauge? That is a very inaccurate method, made even worse by the rubber bladder in the US Gen2 gas tanks. Miles traveled divided by the gallons you put in at the pump is most accurate, but best if averaged over several tanks (because of the bladder). The MFD is fairly accurate, much better than going off the gas gauge.
No gas/diesel car is going to get good mileage with your driving distance. The best way to increase your mileage would be to walk or bike the less than 1 mile trips. Otherwise, 32MPG is about what you should expect. A grille block might help heat it up faster, but 1 mile is still a very short distance.