I think it works both as an expression of parenting anxiety and as a cautionary tale about anxiety itself it being like a baby you nurture. In the opening sequence we see the sperm come from Henry's silent scream - not arousal, but fear. The planet with the man appears to be inside Henry's head and he reacts in accordance with Henry's gasp to whatever's outside his window, pulling levers that appear to direct the sperm into a puddle, which I'm gonna say is Henry's subconscious.

Given the movie's title I think the dream sequence where Henry's brain gets turned into erasers is important. I think it has to do with memory loss/repression. Henry's own bricked out window could also be read as a symbol of repression. Actually if you google 'eraserhead window' there's an extensive theory about the importance of that window and what's behind it.

Couldn't tell ya about the chickens and the radiator lady though.