Hi!
How would I go about using a property from within a group of shapes?
And is there a way to set a property on a group which is then usable by its children?
The white/pink box below is a group of shapes. 
Shapes that are not linked to anything in Visio shape data are always shown as pure unlinked visuals in DataMiner Cube's Visual Overview. This includes children of that unlinked shape.
In your case, because the pink shape's parent is not linked to anything, the shape data of said shape will also not be processed.
You can easily resolve this by linking your group shape to your element or view in question.
I do want to note that I'm now wondering if we shouldn't adjust this so children that do have relevant linked shape data are shown correctly regardless of whether their parent is linked. You can rest assured that I will follow this up.
Pagevar is the way to go, but again I like your thinking! We could introduce a session variable that is limited in scope by its shape group!
Awesome, thank you! Per my other question: is there a way to set a property on a shape group and use it by the children shapes or is PageVar the way to go?