His first try produces the reverse list. Why? Well, he wrote an internal recurring function which takes the unprocessed (unsquared) list as its first argument and accumulates the result in the second argument. The accumulation process takes the square of the first argument of the unprocessed list and conses it with the already-processed result. Now lets examine a simple case of list-square'ing a [1 2] vector: 1. things = [1 2], answer = nil 2. things = , answer =  : nil 3. things = nil, answer =  :  : nil
Second try isn't much better. Lets see what happens: 1. things = [1 2], answer = nil 2. things = , answer = nil :  This shouldn't even work, as (cons nil x) doesn't make any sense.
Performs an f for every x in xs and returns a nil