I’m not sure whether this is the reason why I found the pre- and post-mission parts more interesting than the mission itself, or whether it’s "all I know about Redwall I learned from reading PPC missions, so I don’t care much".

Crash Dummies aren’t necessary? Agent Cadmar and some others disagree.

Yes, meta-fictionally, you don’t need a Dummy. TOS and early spin-offs don’t use Dummies, because Araeph had not invented them yet. If handling the Dummy would distract from the mission, you can get away with ignoring the fic’s first person nature, even when it’s obvious from quotes. (The Agents probably forgot the First-Person Dummy or don’t even know about it, because they were never properly trained, and they got away unpossessed because the Sue Wraith preferred acting out the story in a corporeal projection – because who understands the proceedings of a Wraith?)

But Natalie remembering the Dummy and leaving it behind, just because "somebody" told her that it isn’t really necessary makes her look either stupidly reckless or recklessly stupid to me.

The ferret thought several random things ...
That’s a colloquialism I’m guilty of using too, but shouldn’t she actually have "thought several random thoughts"?

... which then led to some very random thought about animal-heat relief.
Combined with "some" (not "one"), these should be "thoughts" (plural). Did you try to avoid repetition when you made her think "random things" earlier?

I always knew Restoration, but it was buried from fear.
I would have said "by fear", but maybe Khajiit talk like this?

And then Za’kiir is stupidly reckless or recklessly stupid just to check whether he learned healing. May you be up to something there?

HG