I think I can do this from looking at videos, but first I want to take a peek.
Is there a trick to getting these plastic rivets off, or are they meant for one time use and I just need to break them off?

 

Those stay on the car, you'll need to remove the allen key fasteners holding the fender liner to the bumper to get access. IIRC they're 4mm hex

 

I found a good video about those plastic clips with tool suggestions. . But I'll try pulling that panel back without removing those rivets as you suggest. Thanks!
I've got allen wrenches so that should be fine.

I'm using this video showing how to get access to the pump , and in it, all those plastic rivets were already broken off and it's just hanging on by wire. Certainly made it easier for him.

It looks to be quite simple, except for the awkward access. I'm hoping the video makes it look harder to see things than it really is.
I'm leaning on ordering this ACI 177138 Windshield Washer Pump , which is the same one that AutoZone sells, but cheaper and with free shipping. (Unless I hear that it is a crappy replacement.)

 

FWIW, you can buy all those plastic rivets/fasteners in bulk on Amazon. I keep an assortment in my garage, so when I remove a trim piece and break a fastener or push rivet, it's not a big deal. Also avoid wiring your junk together like the guy in the video.

 

Since your there,great time to upgrade the foglite bbulbs w/ led ones........

 

Thanks @MattRX, it was exactly like you said, just the lower bolds, than bend the plastic.
There are in the RX400h 3 pumps, for the windshield it is the lower right one.
This one did the job for me: Had to send another one back.

Best,
Cornelis