I apologize in advance if this has been answered somewhere, I've looked through posts and FAQs and did not see anything.

If a hero uses a feat and the overlord plays a card on the same event, is there any order that these must be played in? Here is the example:

An overlord attacks a hero with a monster. The hero, being low on health, plays his feat card, which increases his armor by 4 from a base of 4, to a total of 8. The overlord then plays his Critical Attack card, spending 8 threat, giving his monster's attack 8 pierce.

If it was necessary for the overlord to play any of his effective cards before any feats, then he would most likely only spend 4 threat and thus the feat would have some effect in this example. Are there any rules for negotiating this or is it just whoever chooses to play their card first?

i would say it just comes down to whoever plays their card first. this would be the same concept of "killing blow" (set dice sides to whatever you wish), being followed by a dodge card, which would negate the use of the card. (a smart hero would have aimed first however. )