> Puzzle 4. List some interesting and important examples of posets that haven't already been listed in other comments in this thread.

here is my take on the question.

1) In a operating system (or language env. like nodejs) -- a set of packages.

For example all versions of all packages form a set. There is a dependency relation between some packages, and in some other cases -- there is no dependency relation at all
The dependency relation is uni-directional (in the sense that Package B depends on package A, can be viewed as PackageB < PackageA ).

Because the relation does not exist across all the entities, this is partially ordered set.

2)[This example is not correct. See comments below. ]
In Borrower-Lender business relation. Same thing. There are some borrowers and lenders that can be represented as B1