I've tried posting this ten times but lost it each time.
I can answer bullet points but main question:

Can sociopaths love their children?

Bullet points:
Ex husband and I met at a MENSA gathering and he is far more intelligent than I am. We have a daughter. I've always believed him to be a sociopath (as does he - proudly. He believes it's a step forward in evolution.) He is highly successful and charismatic and everybody loves him. I do believe he loves her.

+She is very much like him in intelligence, personality, and looks. People joke-ask if I'm sure I'm the mother. I believe she is the only person on the planet he thinks is his equal and worthy of that consideration. I do believe he considers her his equal which is really saying a lot if you know how he really thinks about most people including family and friends.

+I cannot say for sure if he would sacrifice himself for her like I would but I guarantee you he would sacrifice every other being on the planet. He would never hurt her. (Intently, I'm not counting that he doesn't see her very much because he doesn't see that as hurting her because being away from another peson never hurt him any.)

+He does sacrifice financially way more than he has to in order to support her - and me, because he tells me I'm providing a valuable service raising her for him. People tell me how lucky I am all the time for all he does. (And I am appreciative.)

+I believe he's a sociopath because he told me he taught himself to react to fit in because he really doesn't feel things like other people. In addition there were childhood behaviors including attempting to kill another child when he was five which was covered up as not knowing what he was doing, but he told me understood death before that, just not that he would be subject to consequences and that was the main lesson he took from that. He says he recognizes others have an emotional reaction to hearing about others getting hurt or any of that, but he simply processes it and sees if he can benefit and what reaction he should output. He described it as an intellectual exercise that he does take quite a bit of pride in being very good at.

+Unlike some of what I read on sociopathy, he is not out of control. He is highly in control. He considers everything he does and acts only if he gets more benefit that negative out of it - he has broken the law but not frequently and never in a way he could get caught. Mostly he considers it a waste of time with an inappropriate risk reward ratio. No one would ever know that except me. He is highly successful in his career - prone to boredom and slowed his progress a little job hopping but he is so very good at everything he does that he is still far above most his age.

+He says he loves her and he never lies to me about anything - including the way he thinks about other people in ways that disgust and horrify me. We divorced eventually when I got psychological help from my highly abusive childhood and could no longer deal with the admission that he didn't love me, but he found me more tolerable than anybody else he'd been around. (He never abused me which back then was a big jump from anybody else I've been close to so that was great for a long time. Tolerable means not worthless!)

+He is never cruel for no reason. He doesn't care if someone has to be hurt to get what he wants but he never hurts someone for joy. He thinks that's a waste of time. He's one hundred times more likely to help somebody because he finds that type of dynamic can give him a lot of power and be helpful later on. (He explained this reasoning to me.)

I know it is meaningless because it is what it is, but I'm just curious. I would sooner admit I was wrong about him being sociopath than that he doesn't love her, albeit in a somewhat different way than I do. And I would be quite surprised if his amygdala functions like most of ours.
Yet, everything I'm reading says that sociopaths are incapable of loving their children and are a risk to them.