The book The Sociopath Next Door is a good read and short.
As for his depression - yes, I’d be cautious about your son’s time with him. Maybe you can just offer to him that he can skip or have shorter visitations with son 3 right now when he’s so depressed?
And now that he’s arranged the baby furniture - don’t ask him for other help. Who is there who can come stay with you when the baby comes?
