Checking Suspension Components

"About the brake caliper sticking like you had mentioned, what's the easiest way I can check that?"

The way I do it is raise the car and rotate the wheels. If its hard, the caliper may be sticking.
If you have someone to sit in the car and press and release the pedal. Sometimes it only happens when they get hot.
So after driving the car you have to check it fast so you have everything set up and ready.
Compare with the other wheel. If on side spins freely after releasing the brake pedal and the other one
doesn't, it's probably sticking.

Since the pads last a long time, the pucks don't move much and could become stuck. So I will press the
shoe back, which moves the puck back. The press the peddle to firm them up. I will do a few times.

Depending on your DIY skills, you can take them apart and clean them. Or get a rebuild kit, they are fiarly inexpensive.
I use real fine steel wool to smooth out the caliper bore where the seal was sticking.

 

Perhaps the clunking noise is the pad braking away from the rotor.
They may be sticking to the rotor. How many miles do you have on those pads/rotors?
The problem we have in Florida, like Texas (I was stationed in Ft. Hood) is the humidity and/or rain.
The brakes are hot, even though they are cooled by the rain, they get surface rust on them.
When everything cools, the pads "sticks" to the rotor.
If it's bad enough, you can either replace the pads if they are getting low, or do a figure eight on the concrete
to rough them up. Or use some medium grit sandpaper to get the top layer cleaned off. Then also clean the rotors.
Both sides. You're basically cleaning off the glaze. I do that when I replace the pads anyways.
If they car is not driven a lot, or has sat a while, the rotor can start to pit and you'll feel it when you apply the peddle
lightly, a pulsing. Most of the time, depending on how bad it is, the sanding will clean it up and normal driving will
keep it clear.

Looking at the photo you sent, the caster is nearly a full degree off! If they even out the camber and toe, it will likely
bring the caster closer to normal.
The left/rear toe is off also, a lot.
Ideally, you want all those numbers matching.
I don't know what the specks are for the Prius. But if the camber calls for "-.2", then both should read that.
If the caster calls for "+5.9", then BOTH sides should read that.
And I'm guessing the toe would be "0" or "-1"

The best I can see from my 2010 Prius is there is no camber, caster, or toe adjustment. It is fixed.
so if it is off, then something is bent, or a bushing is worn, which may not show on an alignment, but you'll
feel it driving. But the left/rear toe is way off. I would suspect something is bent, slightly, bushing or wheel bearing.
Or combination of the three. There is a bushing on each side for the whole axel assembly for the rear wheels. I forget what they
call the whole thing though, brain fart!

You said you hit something and damaged the right rims. I suppose you might have damaged the steering rack, and/or
tie rod ends. But if the steering seems smooth left to right I doubt that it's bad. It is electric, and it might of gotten knocked
out of sync and the computer is trying to correct it, maybe getting a false reading.
You would see a lot of play if the bushing were bad, harder to see all the bushings in the rear though
======
Judging by the 2nd photo, which is a very strange way to do it, it looks like the got the front set okay,
But it changed the rear. Notice the left rear toe was way off but is now centered. And the right was centered,
but is now off. But did you notice it WAS centered, then afterward it's off to the right?
I'm thinking if you hit something hard enough to damage both rims, you could have damaged the wheel bearings, front and/or rear.
It is hard to diagnose over chat. You have to jack it up or put it on a lift and start muscling around the wheel.
It should NOT move.

I'm not sure where it is, but there is a supposedly a very good hybrid shop in Texas. Someone here knows it and hopefully
will let you know where it is. And you are close.

 

I know nothing about that company so can't help their.
Someone had mentioned it in the past week and I don't remember where or who. Sorry

I don't think the rear has any adjustments, unless a frame shop does it.
It's kinda weird that after the front was set, the rear changed so much.
You did mention the toe kept going out. Which would say maybe the tie rod ends, both inner and outer.
Again, hard to give better answer with out inspection. You may just have to take it to Toyota and explain
to them what's happening and hopefully they can find the problem.

 

Sorry, I wished I could help you more.