First off, I butchered the spelling of Gaal Dornik so I apologize for that. Second off I am going to speculate on something that could have major spoilers so turn back now in case I am right or wrong.
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Speculation and Possible Spoilers begins here. Gaal is narrating about things from a retrospective perspective. She mentions Stars End and The Mule in passing. She appears to have a certain intuition about her as well as the unlikely luck of not only escaping from a planet where religion has curtailed science, but in spite of her removing the sacred metal pieces from her face, seers or the religious leaders of her world still communicate with her. She is an outcast on her home-world, but the seer on Trantor still agrees to sit with her. Later she bravely joins Hari Seldon in speaking truth to power by supporting Hari’s hypothesis in direct opposition to the Emperor. Note that the Emperor is capable of having people executed who have devoted their lives to him just for being in position of literature related to Seldon’s predictions and yet this murderous man gives Hari everything he wanted and he does so feeling as though he has taken the best advantage of the situation. This is a guy who only cares about preserving the “Empire’s Peace” which in my opinion is just semantics for “Power.” That is all Cleon wants and enjoys.
Now at the end of episode 2, Gaal got shot out into space, presumably for what? Well did she leave behind any genetic material for the child she conceived with Hari’s adopted son? Is the woman 35 years after the flashback related to her?
How is it that Gaal seems to cautiously move through crisis with grace? I suspect she is going to have a role in setting up the second foundation at Star’s End and those of you who read the book all know what I am talking about. Perhaps she is not consciously aware of it, but what if that was the reason why Hari also chose her. Is she going to start the Second Foundation?
My theory about the ending of ep. 2 is that Hari Seldon recorded his mind in an AI (that would be the thing on his ear), and Raych knew about this, and there was some sign that the recording was over, and that's when Raych killed him. This would be consistent with Hari Seldon sticking around for the whole series, which I expect him to do, and as consistent as possible with the books, where there were recordings of Hari Seldon to guide the Foundation. Why would Raych kill him in a bloody way if my theory is true? Well, maybe in this universe when you record yourself in an AI you just become the AI, and the AI has control of your body. In which case, a bloody killing may not even have been painful for Seldon.
Gaal in the books actually goes to Terminus, but then, Gaal in the series possibly has also Wanda in her, and Wanda was the one that established the Second Foundation.
I hope Salvor Hardin isn't Gaal's daughter, in spite of all the hints. I just wouldn't like this series to go the Star Wars way, where all the main characters end up being related. If it's supposed to make it easier to relate to them, it doesn't work for me. It just makes me think: "Oh, no, another universe where nepotism is rampant!"