Mun’s Theories:
who cooks normally?: Hakuba. He probably let Shinichi cook once, and that was that.
how often do they fight?: Once a week, depending on how lonely Hakuba is feeling. More often otherwise. Occasionally have a BIG FIGHT. Hakuba probably always gives in.
what do they do when they’re away from each other?: Work, work, and more work.
nicknames for each other?: ’Half-brit Half-wit’ for Hakuba (or just ‘Hakuba’), ‘Meitantei,’ for Shinichi.
who is more likely to pay for dinner?: Hakuba takes care of the bills. All bills. From whatever account.
who steals the covers at night?: Shinichi.
what would they get each other for gifts?: Books. Just one each for special occasions.
who remembers things?: Hakuba, mostly. Think of this as a Sherlock Holmes and John Watson relationship. Shinichi’s too busy being brilliant to worry about stupid domestic details.
who cusses more?: Probably Shinichi, since everything is ‘kuso this’ and ‘baarou’ that.
what would they do if the other one was hurt?: When Hakuba’s hurt, Shinichi mutters and helps him when Hakuba whimpers and asks. When Shinichi is hurt, Hakuba goes about taking care of while trying to get him to calm down because he’s probably raving about how great things were or how frustrated he is. ….damn.
who kissed who first?: Hakuba kissed Shinichi because Shinichi probably never would have otherwise.
who made the first move?: Hakuba, most likely, forever after that first kiss and stealing more kisses, like a very, very patient vulture.
who started the relationship?: Hakuba finally broke down and asked him to give him a straight answer after hinting forever and Shinichi shrugged and said “I guess?”
Hakuba’s Thoughts:
“We’d probably be most happy when working on cases together, but I would have to get used to losing and feeling ignorant… all the time. And never being impressive or good enough. A downward spiral of inadequacies and insecurities? I admire him, though. So much. And he is very kind and so brilliant. I’m just not good enough for him.”
….
((I used what I know of canon + my conan from askconan + the Shinichi from askkudoushinichi to form these answers. My Conan is demanding to know where the hell Ran is in all of this. So, as always, take these theories of mine with a truck of salt…))