Who proposed? If we’re being technical, Howard Stark.
How did they propose? Jarvis was under no illusion that what he did to get Ana out of Budapest wasn’t going to result in very bad things for himself, and, with that in mind, did not propose to her, figuring there was little point to it. He told of his affections, in his understated Jarvis way, but he didn’t make any plans for the future. This had the effect of making Ana slightly (not much, just a little) uncertain about how he felt about her, and wondered if he was just being kind or felt obliged to help her out. Once Howard stepped in to free Jarvis, he was under the impression there would be epic kissing and wedding bells, and was very disappointed when all he got was Ana tearfully making out with Jarvis, and then awkward stammering about what might be the next step.
Howard: Wait. Wait. You love her right?
Jarvis: Ahem. Yes. Very much so.
Howard: And you love him, right?
Ana: Yes! All of him!
Howard: Okay, then, well I did not put myself out here for there to be no happy ending, so if you’re not getting married, one of you marry me. Someone’s having a wedding!
And Ana and Jarvis agreed that it should probably be them
Howard: Great! I’ll get the rice!
Who stressed more over wedding planning? There was no wedding planning. Ana and Jarvis were married in a civil ceremony in Liverpool, and the only thing that required any planning was Ana finding herself a wedding suit (Howard paid for that, and got her a bouquet because ‘girls need flowers when they get married’). Jarvis had enough money stored away to buy cheap wedding bands, with a promise to get Ana a proper one--and an engagement ring--once they were settled in their new life. They both got their current wedding bands on their first anniversary. Howard's often remarked they really should do a 'real, big wedding', especially now the war's over, but so far, neither of them feel it's important.
Who had the wildest bachelor(ette) party? Neither of them had one, though Howard bought three rounds for all the patrons in the hotel pub later on, in celebration. Jarvis was the least drunk person there.
Who freaked out before the wedding? No one. Once they made the decision, Ana and Jarvis were very sure of themselves, and, considering how stressful life had been, having a wedding was very relaxing.
Best man/maid of honor Howard gave Ana away, and acted as witness. He also came through on his intent to get rice, much to Jarvis’ horror (those are worth ten ration points!). Jarvis stopped him once he’d thrown one handful, and confiscated it, finding a family to give it to, who might eat it and not throw it on the ground.
Howard: You and I are going to get along great, I can already tell.
If/what they wrote in their vows? Ana and Jarvis merely repeated what they were told, though they both had a bit of trouble with the other’s last names.
Jarvis: I really should learn how to say it properly.
Ana: It doesn’t matter, I will be Yarwish now.
Jarvis: Yes, well, you might need to work on your pronunciation, too.
Who cried at the wedding? No one, though Ana cried later on, once they were on the boat and she was alone, so as not to concern anyone. Happy tears, mostly, but also a few sad ones for everything she’d left behind.
Which song did they have their first dance to? "How High the Moon" by Benny Goodman. It was playing on the radio in their cabin. That’s when Ana learned that Jarvis is quite a good dancer.
Where did they go on their honeymoon? America! They had four days on the boat over there (a supply ship Howard had commandeered for himself), and Howard insisted they take the time. Ana suffered a little mal de mer, which made her woozy and kept her confined to her cabin a lot of the time. Howard declared that to be ‘as it should it be’ and suggested that they ‘make the most of it’. They did, in fact, make really a great deal, if not the most, of it.