I've pondered on this as well and agree that you should not be able to shop, etc, whie dead. But yes, your idea about being able to view the your ability tree or shop items would be great.
Here's a screenshot.
I was playing against all Rook's and noticed that quite often two rooks would share the exact same space so it only appears there is one rook. They would walk at the same time and occasionally get out of step so you can see there are two. Personally I don't care for this and would prefer that they could never share the exact position and would have to be at least one half their size away from each so you could see there are two. Again. Game is looking great so far.
It appears that the AI teleported in between their towers and was stuck there until he died.
Also, when you Alt-Tab back to the desktop, I see the name is called "Forge". Shouldn't it be "Demigod".
I have a small UI issue that I think needs resolved and should be easy. When I have an enemy selected (especially another Demigod) and I click on a shop to purchase an item. The little item at the top of the screen that shows which enemy you have selected is displayed on top of the screen that shows the items in the show overlaying on top of the first item in the show making it difficult to see it and select it. The window for the shop items should display on top of the