You should be able to assign the F1-12 hotkeys to potions, skills and weapons - open the appropriate menu, hover over an item and press the desired key (ie assign F1 to restoration potions, etc). CTRL-F12 will bring up the window to assign hotkeys (or you can go through the main menu).
CTRL-F11 will save a screenshot (in png format) in the '..Divine Divinity\capture' folder. Can you manually upload screenshots, or set the software to watch specific folders?
The original release of this game was a year before Steam, so I don't know what would be involved in adding overlay support.
