Yes, I still think as I said upthread that Emil is only one with links to a lot of the people murdered. Basically all people who destroyed his childhood. And one of the only ones apart from Claes to display art knowledge.
He worked at A&L logistics where first murder took place, which also gave him access to that yellow car and would explain why the toy catalogue (which contained items used to stage the murders) Henrik found had the order form missing as Emil ordered the stuff while he worked there.
I reckon he faked his own abduction (I checked there were no scenes with him and murderer lurking in it) and staged it in Annika's house to frame her. I think when he said Annika was lower in foster house pecking order than him, he was lying and suspect Annika was awful to him. Thus his motive to frame/ hurt her.
His flat does not seem lived in - suggesting he lives somewhere secret, with the doll's house?
I think Helle Anker's fertility clinic that she used to run is going to be the link and why he murdered her. If Freddie was a sperm donor maybe? We've been carefully told it is Freddie's wife who's unable to have children, not him.
It's got to be motivated by family, the motif throughout series has been about dysfunctional / no contact family relationships. I can't remember if we know anything of Emil's mother but Freddie being his father would tie in with the theme.