At the end of a character's turn when resetting and drawing back to their hand size, if the player draws an armor card can they immediately display it so it doesn't count against their hand size and they can continue drawing up to their hand size?
So, for example, if a character has a hand size of 5 and has 3 cards in hand at the end of their turn and one of the two cards they draw is an armor can they immediately display it and draw a 3rd card to have 5 cards in hand and the armor displayed?
Or, would the armor count for their hand size of 5 and then their turn ends and then at the start of the next character's turn they could display it?
Yep. There is nothing you can do between the end of "end of turn" effects and dealing with the clock drawn on the next turn.
Since resetting happens between the two you cannot play any power or play any card in between unless something clearly let you bypass the rule. Which is not the case with a standard armor.