2) I think what you're looking for is Unity's fixed game view size, not changing how anchors work with window size. Anchors *should* adapt to whatever resolution you're using, as they do.
If you want to have a fixed window size, look at game view, in the top left you can set a fixed aspect ratio or resolution, then if you resize it won't change the ratio of the gui.
However, in the Scene view, it'll keep jumping back to some default value defined by who-knows-what. For example I have a background that stretches to fill UIRoot (fill screen), that keeps jumping to a 4:3 ratio in scene view and 16:9 in game view. which is somewhat annoying... if UIRoot looked at the Gameview dimensions as a reference when sizing the GUI that might stop?
I hadn't noticed you could set a resolution instead of just an aspect ration in the game view window. That helps a little bit, but the anchors still constantly overwrite the scene if you touch any of the editor windows, which is half the problem.
@sintua first:
I just did a quick test:
1. New scene, ALT+SHIFT+S to make a sprite, ALT+SHIFT+L to add a label.
2. Moved the label, advanced anchor, set the Left side to be anchored to the sprite.
The label remains resizable. Nothing is ever grayed out. Even if I anchor it fully it remains resizable. Are you running some old version?
For me, it grays out the width as soon as you anchor either left or right, and grays out the height as soon as you anchor either top or bottom. I'm using 3.4.9.
1. Why do this? Why not just move the sprite to where you want it to be and then anchor it? Why use numbers at all? If you want to fine-tune its placement, use arrow keys for nudging, just like in Photoshop, or hold CTRL to disable snapping to edges. Numbers are there for those who need them, but are certainly not necessary to create a layout.
Because sometimes we anchor the sprite but then realize we want to change the size, or we set the size and realize we want to change the anchor. And we have to set the size manually by number to make it pixel-perfect since we have to use Fixed Size to stop everything from sliding all over the place when you move the play window.
2. A good UI tool should always be WYSIWYG. I never liked this feature of DF GUI where the editor would look one way then as soon as you hit Play, things change. It's inconsistent, and is a bad idea. As sintua mentioned, set a fixed size on the game view itself. This way everything will look as you will expect it to. Also, multiple monitors with the game view being on a separate monitor is a very useful thing to have. 
It should be WYSIWYG in the scene view. The scene view should not react to the inactive game window at all. No other tool or asset I've ever used in Unity acts like that. Unity is built around the idea that you do all your design in the scene view and then look at it in action in the game view, not the other way around. Scene view should always take precedence when you're not in play mode.
Edit: I wanted to add, I just want the OPTION of having a fixed width and height when designing the UI and to have it not overwrite the scene when moving editor windows. If other people find the current behavior useful, then that's fine, there are already three options in UI Root to get the slidey behavior. There could be one more for "ActualFixedSize" that actually fixes the size instead of just the height.