I understand that this might be the most simplest questions ever, but when using AP, do those AP's dissappear as soon as they are used the first time, or are they regenerated at the end of the turn?

Could you be a little more specific in an example?

Let's say, for example, an Acolyte fires on a target with an armor rating of 4 and hits, doing 6 damage, inflicting a total of 2 wounds. If he attacked again and does 6 damage as before, will it be 2 once again or would it be the full 6?

Armour points apply per hit . Toughness, too, for that matter.

Armor doesn't go away, it's a static number like toughness bonus. So if you have a Toughness Bonus of 3 and AP of 4 from Guard Flack, you reduce 7 damage from incoming shots, every time. The only time I can recall a situation where your AP would go down would be critical wounds, though I can't find the passage or recall where I read it.

Note that if a weapon has penetration, it ignores the penetration value of the weapon in armor points with each shot (it doesn't take it away). With the same example above, if you fired a gun at the person that had a penetration of 3, you'd only subtract 4 from each shot (TB of 3 + 4 from armor -3 from pen).

Also note penetration does not subtract from toughness bonuses. Again an example, you fire a gun with penetration 12 against someone in flak armor with a TB of 3, you ignore the armor (4-12= 0 in this case) and subtract only the TB from the damage dealt.

COVER is handled differently; every time someone does damage in excess of the AP provided by the cover, the AP is reduced by one. For example if you hide behind light wood you get a bonus of AP4. You get shot for 3 damage, nothing happens, the cover absorbs all of it. Next shot is for 7 damage. 3 damage goes through the cover and hits the person hiding behind it, the rest is absorbed by the cover. In addition, the cover took damage higher than it's AP (7 > 4), so it's AP is permanently reduced by 1. For the next shot, it's AP would be only 3, and so on until the cover is essentially destroyed or broken to the point it's not effective cover anymore.