Thanks for the feedback.
There was a direction where you could change the group color from the "shapes tab" but we had to solve it without having this window always around and taking too much space from your precious canvas. We are planning to change and simplify all tool interfaces. The "Color tool" is the first one. The bad news is that it seems like the current implementation fails because you couldn't discover how to select a whole group within the "color tool"
Btw would it be handy to be able to deselect all objects if you tap on canvas?
Changing group alpha seems doable, but it won't change the alpha value in the given color itself, but it would act like a "global" value. So if you give a shape a color with 50% alpha and then you change the alpha of that shape's group to 50% as well, the final result you'd get is 25% alpha for that shape.