Can ability cards be used once per round or once per mission?

Same question but concerning rebel "Strain abilities"

and lastly, if a rebel uses both actions for example moves then takes a rest, can they then also use an item card after? Or does using the item card count as an action?

Pg 2 RRG

"If an ability is “used,” it can be triggered multiple times each round, but it can only be triggered once per timing instance."

This applies to all abilities. As long as you can pay the cost to play them (exhaust, strain, deplete etc.) you can play them once per timing instance.

If the item card has the special action icon on it, it requires an action. If it doesn't, your example would be accurate.

This totally depends on the card.

If there is an arrow, it needs an action and is considered a special action. Then it can only be used once per activation.

If the card is exhausted, it is turn sideways and will be readied again when that hero activates the next time.

If the card is depleted it is turned face down and can be used again in the next mission.

If the card is discarded, it is out of the game for good. (or again in the supply deck next mission).

If the ability needs strain, there's no limit.

Often there are several of the upper stuff combined, as special action + strain or strain + exhaust.