I have racked my brain about it and can't find anything online about it either.

Wicked strike says "Target: One creature marked by you".

Yet it also says "Special: You can use the power in place of a melee basic attack".

Now I assume it to mean for such instances as when the fighter combat challenge feature is activated. But what I want to make sure of is whether the special section of the power overrides the target in other circumstances such as when a warlord power triggers a melee basic attack.

you can use the power whenever you have a target that meets the criteria.

What is the prerequisite for the attack? That your target is marked.  The fact that it can be substituted for a basic melee has nothing to do with either the source of the mark nor the conditions which allow you to take a basic melee attack.

Attacks of opportunity, warlord abilities, actions points, utility powers, charges etc. All of these situations allow (sometimes force) you to take a basic melee attack and if you have wicked strike and your target is marked you may choose to instead use wicked strike instead of your basic melee.

When you use an encounter power you no longer have that power for the rest of the encounter. Some abilities may allow you to regain its use in that encounter but otherwise its type dictates its availability.
1) at will
2) once an encounter
3) once a day

The fact that its the same turn (because of an action point) doesnt have any bearing on determining if you can "reuse" the power.

This is distinctly different from an ability which may say "until the end of your next turn you may..." In this case the language is pretty clear as well. If you were traveling with a bunch of warlords and had an action point you may be able to use the ability granted by the power several times.

Remember though that when describing your character's actions you aren't bound to the rules text. Your "Wicked Strike" could be a grazing blow while your "basic attack" could be the dramatic slash across the maw of the giant lizard.

Just as in old school Dnd a "Hit for 4 damage" could be anything from a "miss" to "cleaving a torso in two" depending on the target and circumstances.

When the damage is negligible and the DM chooses to roleplay it that way.

One big issue with HP games is the death of 1000 paper cuts or healing those cuts.

Using hit points as simply physical damage in stead of luck, resistance, etc leads on to the questions like "how could I not have done X I hit him with a battle axe."

Using various descriptions of damage (including describing a hit for nominal damage as a miss) helps keep the idea that weapons and combat are deadly and more cimematic...especially in high hp environments.

Certainly play-styles and preferences vary and it doesn't make much difference, however in an environment where misses can do half damage and apply additional effects it sometimes is easier to describe action as a near miss when as Kyle put it... the damage is negligible.Every player knows it was a hit but its an effective way to impart rp knowledge using crunch.

Still as a DM I like to use perception checks, fortitude checks etc outside of combat to build a mood...something not codified but certainly effective in adding depth and a meta-verisimilitude to the game.

YMWV.

The princess bride example is a good one...wish I had thought of it. For those who dont know the reference but want to follow along
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Notice how the beginning they name the styles/ maneuvers each is using?  Heh if that's not 4th edition Im not sure a better movie example could be found. I think thats the kind of thing 4th does easier than prior editions.

I would guess this is about 8~10 rounds? How many "hits" do you think happened in those ~10 rounds? Now this is rather a stretch but let us assume each used an action point for a total of 22 standard actions.

Assuming equal level (why not) 11 of those should have been hits. Further, each probably used at least one encounter power so likely we saw 11 hits plus 2 half damage misses. Yet we saw no action which we would have been called a hit "story wise" until the disarming. I'd hate to think such a cool scene is merely the result of epically bad rolls.

Still it is a matter of styles. Some grim or gritty games like to keep track of every little scratch, apply separate healing factors depending on original severity of the wounds, add massive hp loss instant deaths and keep all manner of statistics to make the characters feel realistic.

I much prefer to have a character's story arc, personality and motivations breathe life into a character. Of course these approaches arent mutually exclusive and each DM has to find their own blend. For me, I find that there are only so many things I can lend my attention to and I'm much more interested in the creative aspects rather than the minutia of wounds, combat or weather systems. (heck if I want to have it rain story-wise why bother with the "fairness of when it rains" make it happen captain.

I guess its almost like focusing a movie camera when directing the fight scene. You could zoom in on each hit and show the wound in all its "high def" glory or you could pull out and get the essence of scene and have a singular dramatic element.

Everyone at the table knows the halfling didnt do too much of the damage to the t-rex. Still its much more satisfying (to me anyway)  for him to have slit the stomach of it open spilling its entrails all over the cobblestone plaza-causing chants of admiration from the spectators. It works better in my game story-wise than for him to be responsible for the 15th cut of 10 hp or more which happened to kill it.

You can describe it anyway you want and I dont think there is a right answer. I see how some players might feel "cheated" if their hit for 10 damage merely bounced off the creatures hide or the arrow stuck into a shield etc.  I find however that those types of players generally dont enjoy the same aspects of the game as I tend to focus on so I imagine its sort of self segregating.