Nucky's clearly having some psychological issues over killing Jimmy. The child's seeping bullet hole perfectly matches the location of the first shot that dropped - but didn't kill - Jimmy in the last season finale. Nucky's known him all his life and has been a surrogate father - I have no doubt that was supposed to represent Jimmy as he looked (or at least as Nucky remembers him) as a child.
I think Billie is definitely real, but Nucky's relationship with her may be an extension of his growing dementia.