You've pretty much nailed the problems I had with this story (and much of this period JSA) in that Johns would just lay plotlines all over the place and just dropped them (even aside from Hector, we have in your post alone - Obisidan and the mystery of the Shadowlands, Sand's infatuation with Kendra and her using him to avoid newly-reborn Carter, Kent and Inza in the amulet). Johns has gotten better at tying up plot points in Green Lantern and I loved JSA but it still bugs.
Let's leave aside the fact that Hector was led to believe - and so were the readers - that his own wife gave birth to him. We are basically explicitly told that a possessed Hank Hall raped Dove to impregnate her and their son (despite neither having the same DNA has Carter Hall) looks just like the old Hector just because his soul is in the body. Which did not work with Kendra who had the soul of Shiera. Another point even after Kendra found out that the real Kendra was dead and she was Shiera with all Kendra's memories she had basically no interaction with her "son" Hector nor he with her. At all. Or the fact that once she did get with Carter (temporarily) he was basically having sex with his (through his wife) own great-niece. Ewww. And then as you say Dove disappears from the book, she has no interaction with Hector after this and the fact that she was raped and had a child while in a coma is never brought up again - even when Geoff Johns himself used her in Teen Titans. What a mess.