First guesses maybe:

Puzzle 1

> catMap x f y = catMap x f catMap y?

Puzzle 2
> id = return ()?
> (.) = something to do with (=<<)?

I didn't understand what not sharing meant?

ACT has already given me much of the stuff I've wanted for years.
Especially many thanks MD and JGM for these incredible lessons :).

(Gone for breakfast!)