1. It is completely valid for a texture to only have 1 mip level, and still get sampled with mipmapping enabled. It may not be as efficient as it could if you used a different sampler state, but it's still valid.
2. Sure, you can re-use the same sampler for those cases if you just want to sample them with filtering.

For things like your G-Buffer, you typically don't want to use a sampler at all. Usually you don't want any filtering at all, and you want to sample using a pixel coordinate instead of [0, 1] texture coordinates. This can be easily done using the Load() function, or by using the array operator []. Here's an example:

Texture2D GBufferAlbedo;
 
float4 PSMain(in float4 ScreenPos : SV_Position) : SV_Target0
{
    float3 albedo = GBufferAlbedo[uint2(ScreenPos.xy)].xyz;
 
    // ...do lighting stuff
}

Interesting. Is there any performance penalty to sample for example a textureCube (for shadowmapping) with no mipmaps with the sampler I posted? Does a sampler with more mipmap filtering incur any extra operations no-mipmap textures?

It depends on the hardware and driver, so I can't say for sure. It's also not something I've tested personally. However using anisotropic filtering is definitely going to add a performance cost.

Since it's a shadow map, you should consider making a new sampler that uses D3D11_FILTER_COMPARISON_MIN_MAG_MIP_LINEAR or one of the similar variants. If you do this, then you can use SampleCmp in your shader to get hardware PCF.

ALSO - you cast the screenPos.xy into uint2. Is this because of precision issues, or why is it?

The Texture2D array operator takes a uint2 as a parameter, so I use an explicit cast to prevent warnings.