Kasim's parents (Spoilers) and why they're central to the story
My theory.
Kasim is the son of Nessa and the man with the burned face. He was one of their captors when they were hostage. I assume Nessa was raped but we'll see. (We can safely assume Atika is not Kasim's mother. The DNA test did not have any of Kasim's DNA, the toothbrush was new, and so is irrelevant.) Why is this important?
Nessa is the older of the two Stein children. In theory she and her heirs will get the bulk of the family fortune. We can assume the hostage takers, and Kasim's father, are Palestinians. The Stein family simply cannot afford, politically, to have a half Palestinian child with a legal claim on the family name, reputation and fortune.
Before sending him to his death Nessa gave Nathaniel a message via her assistant (Frances). She said "you were right about what you saw". I think this refers to him saying he saw "rage" in Nessa which was odd for a peacemaker.
I think Nessa has no love for Palestinians. They killed her father in front of her, they kept her hostage for over a year and she has borne a Palestinian son; the knowledge of whom could destroy the Stein empire. I think her captors forced her to agree to use the Stein name and money to help Palestine in order to keep her secret. I think she is full of rage at being forcibly comprised to play the role of peacemaker to a people she now hates.
I don't think this is going to end well ;)