If you can think of a ship, I will answer these questions for them:
who cooks normally?: Gou, since she thinks Seijuurou would be too clumsy for that — even though he isn’t (well, not really) and actually keeps her company while in the kitchen, usually helping her reach the cabinets and shelves, for example.
how often do they fight?: it’s rare for them to have a serious fight, but they commonly argue over such little ordinary things — mostly starting from Gou’s part than Seijuurou’s.
what do they do when they’re away from each other?: send post cards with cute kawaii desu messages as well as letters, and always bring many gifts for each other even if they’re really simple.
nicknames for each other?: Seijuurou likes to call her hime or queen g (referring to queen bee), but never lets the opportunity to tease her by calling her uke slip past, whereas she unfortunately doesn’t have anything to tease him about and keeps it at a simple prince-kun.
who is more likely to pay for dinner?: Seijuurou, obviously. he wouldn’t ever let Gou pay for dinner, since she’s like a first lady for him.
who steals the covers at night?: Gou, and, of course, Seijuurou lets her — since she’s petite and is more likely to feel cold during the night.
what would they get each other for gifts?: he would get her some new hairbands or clothes — mostly floral dresses. as for him, she’d buy or even bake him some fine sweets, because he’s constantly remarking how much he likes it when she bakes something to him.
who remembers things?: surprisingly, Seijuurou. they both have busy lifes and roles on their respective swimming clubs to manage but Gou usually gets more stressed out than she should, and so that leads to her constant forgetfulness regarding things which aren’t related to the club or with her studies at all. on the other hand, Seijuurou is pretty relaxed mostly for the reason he’s more experienced on that subject.
who cusses more?: Gou commonly cusses, but it isn’t even closest to Seijuurou.
what would they do if the other one was hurt?: try to comfort each other, of course. they are this kind of couple where "your pain is my pain", and if one of them is sad and such, the other will also be until they do something to make one another feel better.
who kissed who first?: Seijuurou kissed Gou in their third date, in an ever so flustered manner which made Gou go red — and erupt in giggles.
who made the first move?: Seijuurou, of course. even though there almost wasn’t a second move — mainly because Rin wanted to kill him.
who started the relationship?: Seijuurou, ever since the moment they’d first kissed. and Gou didn’t think twice after saying yes.