Rika

1) Figured this out.

In the meantime, have some post-canon, pre-relationship zutara headcanons:

Zuko genuinely loves The South Pole. Because of the tribe's way of life there's always something to be doing (something that isn't looking at documents). The people, after an adjustment period, take him in their stride. No ceremony, no bells and whistles. It's as simple as one of the grannies looking him up and down, pointing her mitten at him and saying "you, come and fix this." And walking off without another word, expecting him to follow, which he does. After that, all the grandmas of the tribe are getting him to do odd jobs. Like think this picture but in WT clothes:

Then the children notice that he's a firebender and start either forcing him to do tricks for them, or curling up and falling asleep on him since he's so warm. This usually ends with one child or another hanging off of him, regardless of what he's doing. He was very nervous about this in the beginning, but now he just gets on with it. Katara still watches fondly every time though.

The veterans are- understandably- the hardest to win over, but following Hakoda's lead they begin opening up to him, being frank and honest about their experiences. They show him their burn scars and tell their stories. Zuko would rather spend hours in conversation with them than with any of the old nobles back home.

As Ambassador, Katara lives in the newly constructed SWT embassy a little ways outside the palace, with three other women and two men (Including Bato, who was the ambassador before her). The Fire Nation Court are starting to think there's something very strained and tense going on between their nations because the Firelord is always finding excuses to go and spend time there, much to the other ambassadors' amusement. There was an awkward incident when Katara wasn't actually there so Zuko was left pretending that they needed to open 'snow-trade' because it was the first thing he could think of. (Bato didn't come to his rescue at all because he was busy dying laughing in another room).

Katara isn't entirely innoccent however, as she is often seen sneaking back into the embassy at stupid hours of the morning like a guilty teenager, because her and Zuko just couldn't figure out one diplomatic issue or another.

Zuko loves it when Katara humbles stuffy advisors and Katara loves it when Zuko subtly bends old, pointless rules to help someone who would otherwise be left out to dry if they followed policies that'll take months to change.

They regularly go on tours in disguise, seeing the Fire Nation itself and talking to its people one-on-one; maybe getting a lil vigilante action in there as well ('Zuko you're the Firelord, why don't u do this legally??' 'Less fun.')