Are these new plastic rivets supposed to be used more than once? I'm not sure of the rivet puller is meant to destroy the rivet as it removes it, and then if a new one is meant to be installed at that time.
The original Toyota ones can be re-used many times. They will break if dirt collects in them and fills up the gaps between the 'leaves' so that they don't expand or contract properly. That usually only happens with the ones used on external trim parts, not so much in the cabin. Normal usage is to push the center button until it clicks to allow a very gentle extraction, then when they are out in your hand you push the point on the backside of it to reset the center button to the normal position. Then the entire rivet assembly can be clicked back into the trimpart and it will seat and lock properly until the next time somebody pushes the center button.
Some other rivets I had bought to use in my 2014 Elantra have a Philips screw in the middle but these new ones I got on amazon for $7 are as you describe, and the middles are pulled out. They pop nicely into place in the condition they come in, then the middle button seems to lock them in place when you push it in. Finally I'm a master of plastic rivets. I should have enough of these babies to last me until about 2050. The splash pan on the Elantra had to be taken off to change the oil and filter. I was glad to see the Prius has open access to the oil filter and drain plug.
I don't know if that's a change from your model year to mine, or a lost item. Mine has a removable plate about 10"x4" held in by 4 self-tapping screws set in speednuts clipped to the edge of the main splash shield.
Yeah that's the main killer. If you wash them out every time you've removed them, they'll last a long time. I find the next way they fail is one of the teeth starts to get too spread out, maybe zigged-instead-of-zagged when you pushed it in, eventually weakens and breaks off, or just becomes a pain to install. Either way, I'll typically get a full replacement set, then just start replacing the worst offenders. Put a silver Sharpie X on the replacement fasteners, so I can keep straight which I've replaced, over time.
Mine's all covered with a big panel from the rear edge of the front dam to the forward ridge of the front subframe; wider at the front. I can't tell you if you are missing one or if they just didn't include it on that year/trim etc.
They apparently added it on the newer ones. My 2015 is the same as his, which I thought odd coming from the full-size that has a complete cover. I assumed that was to help retain heat for better efficiency but it makes changing the oil a pain so I was happy to see the c was going to be a breeze. I was also surprised that it took a normal filter instead of just replacing the element like the Gen 3 full-size.
In the 5 years and 121K miles I have had to clean this filter twice, and it was easy, but somehow wasn't able to fit the clips back deep enough, so the piece of plastic is kind of dangling ... not to worry - easier to access the fan next time