"Why are you yelling at me?! No, I didn't answer you too quickly about whether or not I have the right ingredients for cake! Dammit, *Hyun-ae, I know what's in my own kitchen."
This becomes almost cartoonish if you live in a one-room apartment or are playing in your kitchen. "Um, it is literally three steps to the refrigerator ..."
Also, there's some inconsistency with the fourth wall: she's incredulous if you tell her you bought a cake, since you're ostensibly out in the middle of space, but she certainly thinks you're capable of trotting out to the space corner store and buying the ingredients for a cake, then baking one up in the kitchen that you definitely have in your tiny spacecraft.
Simple answer to both questions: your ship has a food fabricator and she may have expected you in-story to be using it to synthesize the ingredients, which is why it surprises her when you simply tell her you have the cake wholesale.
Doesn't the Nobility Stipend Amendment - which specifies that "the nobility stipend will only be distributed by patrilineal family lines as officially registered and not paid twice to married couples," - essentially mean they're taking money away from women?
Correct. The whole point of this and other laws and amendments issued by the council was to slowly create the conditions so society aboard the Mugunghwa would eventually evolve into the patriarchal Neo-Joseon dynasty the player met in the first game. For another example, the Motherhood Credit Act, ostensibly approved to increase the declining birth rates, in practice shoos away women from the workforce by making more financially appealing for them to stay at home and have children than to hold paid jobs. This even affects people who didn't want to leave their jobs like the scientist Kim So-Yi, who despite her excellent work she received a pay cut because the department isn't bothering to spend money on someone who on paper is likely to quit and have children in the short termnote (although in this case her dismissal was also strongly motivated by political reasons, because the new Councillor of Engineering and Science didn't want members of the Kim family to keep making a name for themselves in the field).