Has your DK put any of his skill points into active skills?
Learning a skill from a teacher (or a book) doesn't give you the skill directly; you still have to invest at least one skill point in it to be able to use the skill. After learning a skill, it should show up in the list of available skills in the skill window, when you click on an empty skill slot.
There is an icon at the bottom left of the skill window which will toggle between showing all skills and showing available skills.
Once you learn a skill (via teacher or book) any character can invest skill points into it (though you would only want one character to learn Identify).
Setting hotkeys for potions is pretty much the same as for skills.
To the immediate right of each character portrait (in the top right corner of the screen) there is a column of 3 icons, for the primary skill (left hand graphic / left click trigger), secondary skill (right hand graphic / right click trigger) and potions (bottle graphic). To assign a hotkey to a spell, talent or potion you click on the corresponding icon, then in the menu that appears hover the cursor over the desired icon and press the function key you want to assign to it.
If you use a potion hotkey it will only have the lead character use a potion, so if both are taking damage you might have to pause, switch characters and use another potion.
You can pause the game (space bar) if you want to drink non-hotkeyed potions or direct your characters' attacks separately during battle, etc.
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