i know you rb'd it a while ago but if you're still interested in doing it, ship asks (and if you don't actually vibe with any of these ships feel free to skip!)
roy/riza: 8, 9, 15
hawkeye/trapper: 15, 21, 26
margaret/hawkeye: 15 (i really want to know what songs people associate with ships lol), 46, 50
Oh, fun variety with these ones! If it's alright with you, I'm gonna skip #15 for all three (at least for now) because it takes me a while of listening to music while specifically thinking/looking for parallels/vibes with a given ship before I can come up with anything. By the time I do that, I'll forget to come back to my ask box to answer this! So apologies, but also my music taste is extremely old-fashioned so it probably wouldn't be all that interesting anyway.
8. What do they love most about the other? Why?
I think going from a strictly canon reading, Riza loves the ideals that Roy believes in and wants to put in place as reforms. She's dedicated her whole life to helping him achieve that. And in turn, and I think Roy loves Riza's loyalty - not to him, specifically, but to their shared cause. He knows he can trust her above anyone else to see it through, even if she has to go through him to get there. In addition, I think they both find solace in knowing each other so well, having met before the military really entered their lives and changing together through Ishval and beyond.
9. What do they dislike most about the other? Why?
I think Riza dislikes Roy's carelessness most because it makes her job harder because it in some ways betrays their goals. Roy is the one and only person she will ever trust with her father's life's work and the only person she trusts to see the necessary reforms put in to in some way try to atone for their actions in Ishval. She also can't cope with the idea of living without him, so for him to try and fight a killer in the rain without thinking of how severely disadvantaged this makes him understandably upsets her on multiple levels. For Roy, I think he probably most dislikes the fact that Riza clearly can't cope without him, more so because he would hate the idea of her suffering like that in his absence than because he sees it as some kind of character flaw.
21. Do they enjoy domestic life?
So, given it'd be the 50s and they're two men, that's a tough one. I think in the absence of any fear of being "discovered" and discriminated against/arrested, though, they'd get on fine together. They already have experience sharing living space, and in the worst possible conditions. There's little things that would bother each other (just watched "Alcoholics Unanimous" yesterday, and they have a wonderfully domestic spat about Hawkeye using Trapper's towel while shaving and Trapper's toenail clippings ending up by/under Hawkeye's bed), but I think they'd be able to just bicker for a few minutes and move on. The major roadblocks are pretty much external factors (how their relationship would impact Trapper's ability to see his girls, the strain of living semi-closeted in 50s America, etc).
26. What sacrifices do they make for the other?
Given the way the show was written, it's easier I think to pinpoint the sacrifices that Trapper makes and could/would make in a relationship with Hawkeye than the other way around. He's almost always the one getting roped into Hawkeye's schemes or messes (good example is him blatantly committing perjury in "House Arrest" while coming up with a cover story for where Frank got his shiner), and if they were to pursue a relationship back home he would be the one having to give up his stable family life with the wife and two kids unless they kept it secret, and then Hawkeye would be the one sort of making sacrifices there (but I just can't really see that lasting or being something either of them would put up with for longer than just a casual "every once in a while" sort of thing when they happened to both be in the same area). Not that Hawkeye doesn't ever make sacrifices for Trapper (from the infamous "Longjohn Flap" to shelving any sadness he might have over Trapper possibly leaving in "Check-Up" in order to celebrate with him), but it's something he'd have to work on in a serious relationship with Trapper. For the record, I don't think he'd struggle too hard with it, just the way the show framed him as the protagonist and Trapper as his sort of "second" gives it that slightly uneven dynamic. Probably the biggest thing is that, once stateside, Hawkeye would likely have to be the one to move so that Trapper could remain close to his daughters. Depending on where you land as to how much Hawkeye really loves Crabapple Cove or not, that may be a small or a really large sacrifice.
46. Do they consider their relationship casual or serious? Is the answer different depending on who you ask? Why?
Hm, this one probably depends on the circumstances. I think in "Comrades in Arms", Hawkeye was looking for something more casual than Margaret (partly because Margaret was married to Donald at the time, and partly because he liked their dynamic as-it-was whereas Margaret seemed to think she needed to go into Mistress Mode like with Frank or the generals that used to come knocking). I think Hawkeye valued Margaret's friendship so much at that point that he'd rather that not change and they not be together than to be together and have her change her behavior for him. If we were talking post-canon, I think it could almost end up flipped, where Hawkeye might cling to Margaret harder for the sense of familiarity she gives him while she's more focused on figuring out her life post-army. Then again, I could also see them mutually agreeing to a casual thing post-war based on the finale kiss.
50. Would they ever break up? If so, why? Who would handle the breakup better?
Haha, well they sort of did? If they were in a genuine relationship, I could definitely see them breaking up (and getting back together, and breaking up again, etc). The big, unresolved thing between them is their political/ideological differences, which the show really de-emphasized as the years went on and Margaret became part of the "in" crowd less enchanted with the army/the war (compare her clear distress at the idea that peace talks might be starting in an early scene with Frank from I want to say "Dear Dad" vs her commiserating with Hawkeye about the points system being changed to keep them longer in "Peace on Us"). However, without the army/the war as a mutual enemy of theirs, they could definitely end up butting heads on politics again back stateside which could possibly result in a permanent break. I'm not sure who would handle a breakup better, honestly. I think Margaret would handle it worse at first and then probably get over it if she found someone new, whereas Hawkeye would probably be outwardly fine but miss her long after she was gone.
These were all really interesting to think about, so thanks for sending them in! List is here for anyone interested in sending in other questions/ships!