I have started messing around a little with the free version of PIOsolver.

It seems that after a player has taken a bluff-catcher + traps line, he always plays passively until his opponent misses a bet (in these solved scenarios). Is this correct?

Are there theoretical situations where this would be violated, like if a card changed the relative range strengths? I think there must be, like if a player is 'missing' draws? I probably just haven't looked at these scenarios yet.

And what about practical real-play situations where donking turn or river might make sense exploitatively, or, how to adjust to someone who does?

Yes, in many instances. There's no such thing as the order of play in gto and so donking is relatively common.

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The short answer is yes. With GTO play, almost anything is possible, but not everything is probable. (There are lots of lines that feature actions that only happen at a very low frequency).
Where there is a high frequency donkbet, it definitely seems to be related to the change in relative strength of each range, as you mentioned.

Yeah donking the turn actually is a real strategy in some spots, it happens when PFR will check majority of his range on a specific turn run outs i think you bet like 1/4-1/3 pot there OTT i'm not too sure.
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I'm guessing in that spot PFR EV of checking will have higher EV then betting, and yeah when you lead the turn you get some of his EV/the EV of him checking will go down etc.

All ik it's really hard to implement and the EV you gain by having a donking range OTT is small and yeah not sure how the EV of those strategies look like

My best guess is to just x-raise flops to deny equity, your going to have to see for urself what the overall EV is going to look like and whether or not it's going to be worth it depending on a lot more factors such as how villain/population will tend to play