Does Apprentice Magician get its effect if is removed play by D.D. Warrior Ladys' effect?

Yes, since it would've been destroyed as a result of battle.

WHERE it ends up does not matter, which is why this card is NOT a Graveyard activating effect (and thus, the effect goes to the current controller and not the owner of the card).

Using the following Chain Link Matrix

1. Turn Player Mandatory
2. Opponent Mandatory
3. Turn Player Optional
4. Opponent Optional

You fit the effect in the appropriate slot

Link One - Turn Player Optional (D.D. Warrior Lady)
Link Two - Opponent Optional (Apprentice Magician)

Resolve effects

Apprentice Magician resolves effect and Special Summons a Level 2 or lower Spellcaster face-down to the field

D.D. Warrior Lady resolves and removes both monsters from play.

That's nice and all, but that has no relevance on the current question considering that Apprentice Magician only needs to be destroyed as a result of battle and that is determined at the end of damage calculation (before resolving effects).

Yep...people are very used to the searchers and think all of them seem to go to the owner when destroyed in battle.

Not the case here (and with D. D. Assailant). Apprentice Magician, as said, only cares about being destroyed in battle. Where it ends up does not matter and since it doesn't care where it goes, it looks at the controller at the time it was destroyed.

You if it's on your side and the opponent if it's on there side.

So what happens at the end of Damage Calculation?

Is there a magic "inbetween" that occurs saying Damage Calculation stopped, Resolve Effect of monsters destroyed in Battle, then Resolve all other effects in the Resolve Effects portion of the Damage Step??

D.D. Warrior Lady ALSO resolves her effect after Damage Calculation, which means there are two effects that are resolving at that point. Simultaneous effects go on a chain.

THAT'S what makes it nice. Not anything else, and certainly not cynicism.

Where did this come from? I dont think anyone questioned this. I guess its important to have the last word.

Whether they go on a chain or not has no bearing on this question, and it doesn't even help answer it. The question was asking if D.D. Warrior Lady would keep Apprentice Magician from searching out a spellcaster if DDWL removed it from play. The original poster didn't know that Apprentice Magician is not a graveyard-triggered ability or else the question would have never been asked (as they could refer to similar scenarios with Mystic Tomato or Sangan). Knowing that it doesn't need to go to the graveyard, why is there a point in showing how a chain forms? A chain does form between AM and DDWL, and your chain is correct, and even the logic you use to make a chain is appropriate, but that's about it.

If A.M. were a graveyard-trigger (much like in the OCG but that's beside the point) then no chain would even form considering they'd happen in two seperate areas of the damage step and you could treat the situation like you would with D. D. Warrior Lady and Mystic Tomato (for example).

As for your question regarding what happens at the end of Damage Calculation:

My error (which I will admit) was that I said that a monster is considered to be destroyed at the end of damage calculation before resolving effects. What I should have said was: "a monster is considered to be destroyed as a result of battle after damage calcuation but before resolving effects" Forgive me for saying "end" instead of "after," it was a bit misleading.

However, the fact that a monster is destroyed in battle takes place before any effects can form a chain (to keep cards like Hane-Hane from targetting itself with it's own effect if it was destroyed in battle). This happens within the "Resolve Effects" portion of the damage step, NOT in the "Calculate and Apply Damage" portion, in case the rest of you were wondering.

Oh btw, don't mind HDI as he does that a lot. ^_^

Hope that clears everything up on my end.

Actually, it IS partially questioned

"Does Apprentice Magician get its effect if is removed play by D.D. Warrior Ladys' effect?"

It's practically asking if Apprentice Magician has to go to the Graveyard for the effect to work. =\