Divers rulings et questions

Do effects that move tokens trigger effects that respond to the removal of tokens?
For example, if I use a Cloud City Operative to move a focus token off of one of my units, may my opponent play Succumb to the Cold! in response to focus the unit again?

Yes -- moving a token does, by necessity, remove it from its original location. (Nate)

If DS puts Dark Memories on a character who has 1 damage capacity left and that character focuses to strike does the strike resolve before the 1 damage is dealt or does the character focus to strike and immediately die?

The character dies before his strike goes off, because the focus token is applied in step 2 of "resolving a strike" before the combat icons get to go off in step 3.

Q: For the Falcon, you can choose to initiate the ability by paying the cost to return the Falcon to your hand. If you do not have the Character or Droid to put into play, do you put the Falcon back, or is it considered "stuck" in your hand?

NATE: The Falcon stays in your hand -- the cost is still paid in full, but since you have nothing to put into play the effect fails to resolve. There is nothing that puts the Falcon back into play.

Q: So I could choose to pull in my Falcon (say, that it is very low on health) using its ability, knowing full well that I have no Character or Droid to replace it with and simply tell my opponent that I am unable to resolve the effect. The net result is that the Falcon stays in my hand, free to play in a subsequent Deployment phase. Correct?

NATE: Correct. As it's a non-targeting effect, there is no restriction on being able to initiate it. So you can return it to your hand by using its effect, even if you have no Droid or Character. (If you do have a Droid or Character, you are obligated to put the card into play.)