I've played Zelda in Japanese and there's a difference within the translations themselves on how they name items, NPC's or key locations within the game. The quest logs in either ToTK & BoTW in the JP original are written from a first person perspective since it's Link's personal entries while the ENG localization rewrote them in second person addressing the player.

Even the perspectives are written differently: like from BoTW when you read Revali's diary, the Japanese text frames it more around personal confusion and wounded pride as to why a prodigy like him is put in a supporting tier beneath Link. While the ENG localization leans into sharper, more confrontational direct insults, playing up a classic western "cocky rival" archetype.

Yes. Nintendo’s game development group (formerly EAD) is based in Japan with the mothership. The localization team may have input and localize it at around the same time in the development cycle, but it’s written in Japanese first.

How the NOA/NOE teams decide to localize it is largely up to them, though I suspect there’s at least a little oversight from headquarters.

Only tangentially related to your question, but it wasn't until Gen 5 of Pokémon that French, German, Italian, and Spanish started getting their own direct translations from Japanese instead of being translated from the English translation.

Technically not a fully first party game either.

They work together on major titles in terms of planing the differences in advance, but have had plenty of time to figure out works best for each market

I work for a western game studio and hear it’s hard to translate a lot of stuff, I imagine the same is true in reverse

Most yes, but not all.

Metroid Prime 4 for example would have been english-first as it's a Retro Studios title with development support from Next Level Games.

It’s often noticeable how English translated text is laid out poorly because the game assumes all text to be Japanese.

What’s interesting is that the North American studios are actually managed by Nintendo Japan and not NoA. There are interviews with ex Retro Studio employees where they talk about how producers from Japan and Shigeru Miyamoto come into the studio once in a while and start telling the Retro Studio staff what minute things they should change in the game they are working on.

Oh, I wish Revali had been localised more like that. I really, really, hate him and can't stand a moment of him speaking.