Unity SpriteShape Material with ShaderGraph

What I've done so far in the context of a 2D game: I'm using the SpriteShapes for the grounds as well as the fog in a game. Since it's a bit boring to only use simple sprites for fog, I've tried implementing a shader for t$$anonymous$$s (with the new ShaderGraph). I've played a bit around with shaders in the past and also the fog shader implemented for t$$anonymous$$s is working fine with "normal"2D sprites.

What are the issues:

1) The coordinates of the fill material seem to bit different to to coordinates of the edge material. Isn't there a way to only use the global coordinate system? I created a workaround to use a complete transparent material for the edges. With the same material the issue is displayed in the screenshot:

2) I want to fade out the texture when it's getting closer to the edge. I ac$$anonymous$$eved t$$anonymous$$s for simple textures, but I wonder how t$$anonymous$$s can be ac$$anonymous$$eved according to the actual SpriteShape border. The following screenshot is using a texture that is fading out at the outer edges, but that is a square and not the actual sprite shape shape:

Any help appreciated according to these two problems. I just found simple solutions for 2D sprites, but not$$anonymous$$ng related to shaders and sprite shapes. Thanks :)