For example, if a character has the Quick Draw feat and a weapon with a daily which takes a free action to activate, can the weapon be drawn as part of the attack and the power be activated all "as part of the same action"?
"You can draw a weapon (or an object, such as a potion, stored in a belt pouch, a bandolier, or a similar container) as part of the same action used to attack with the weapon or use the object."
In other words, can you use a free action of activating the power in the middle of the attack power?
Same logic would probably apply to using a free action in the middle of a move action.
Best Answer
Yes. If your DM allows it.
You can do as many free actions you like on your turn. However, your DM reserves the right to limit free actions. The only RAW restriction to free actions is that you can only take one free action attack per turn.
Also worth noting as it has been discussed. Free actions can take place during other actions. They are things as simple as talking or making a small hand gesture. If its already a free action you can do it between the draw and the attack, even if the draw is part "of the same action" as the attack.
Lets take a different example. The Warden's marking ability is a free action that can only be taken on it's turn. One of the uses of this ability is that it can be used at any point during a movement, or even a charge. By a similar application of logic you should be able activate a free action magic item power during the course of an attack action (IE right before/during the swing).