Niek, I kinda agree with your problems.
1) I thought the Sheikah dungeon WAS in the shiekah area, you just had to go through the desert and interact with the Gerudo area in order to get to the dungeon.
Honestly, here's how I thought it went, you'd track down the shiekah villages, find a shiekah temple and talk to an elder, who'd inform you of the Shiekah Dungeon's hiding place, but you wouldn't be able to get in without the fire and ice arrows, which the Gerudo are in possession of. So you'd go to the Gerudo valley and (probably learn the last/second to last thief skill) invade Gerudo Fortress, similarly to how you did it in OoT, by stealth, knocking out guards, but here you'd be using your thief skills too. You might also at the end learn some more of the plot, start to suspect that your mentor isn't the good Gerudo king.
Then, with fire and ice arrows in tow, you'd return to the skiehah dungeon.
2) I think they're both reasonable. Death Valley because it's under death mountain, Valley of Shadows because it sounds really cool.
3) MG, how do you imagine the river valley? I was kinda thinking we could kinda combine it with Hyrule field? Just have lower elevation parts of the field with a river running through. And maybe waterways could connect many parts of the world, and certain areas could only be accessed by waterway.
Back to your actual map, Niek, I like the second one better. The whole east side of Hyrule field could be the river valley, if we want to connect Zora's domain and Hylia by a river. I do think it might be better if there were areas on every side of Hyrule field though, but that's just personal taste.