yes , they do it because as you said they are of inadequate size, and or they have erectile dysfunction. he cant get his dick up even tho he wants to, so he'll substitute it with something else
No..
I would say he did that after the murder..
Just to let the Investigators know what he done..
He did it just to taunt the investigators..
Me as a "officially" declared "crazy" Convicted-Criminial should know this kinds of things..