I already specified the monoid part of these monoidal preorders before stating the first puzzle. The puzzles ask what's the preorder part: that is, when does one complex count as \$$\le \$$ another. This depends on what reactions we allow.

Yes, we can think of a complex

$a \text{H} + b \text{O} + c \text{H}_2\text{O}$

as a multisubset of the set \$$\\{\textrm{H}, \textrm{O}, \textrm{H}_2\textrm{O} \\} \$$. Alternatively, and perhaps less stressfully, we can think of it as an ordered triple \$$(a,b,c) \$$ of natural numbers. The monoid operation is just the usual addition of these triples.