For many of the class abilities it states to roll 1d20 in the text to determine the results (Lay on Hands, Spell Checks, Turn Unholy), but in reality I should read that as Action Die - correct?
From my reading, you are correct here.
Also - can a character choose when to use an Action Die? That is, could the Cleric above choose to roll the d14 first when attacking and then use his d20 Action Die second to make the Turn Unholy attempt?
From my reading, the Cleric chooses what Action Die is used by the order of the actions. For example, in your case the Cleric could try to Turn Unholy and then attack, thus ordering the dice as desired.
That's my reading, anyway.