Cole, my answers agree with yours. Assuming that an adjoint exists, proposition 1.88 gives a way to construct it, so I used that, simplified a bit and then verified that the functions I got were the required adjoints.
I think in the case of Puzzles…
Since preorders don't guarantee antisymmetry, I'm a little concerned that meets and joins might not be unique. Is this a case in which category theory only concerns itself with "uniqueness up to isomorphism"? That seems reasonable enough at first, b…