Firstly, the answer is generally:
B) After I roll ALL attacks from a single power but before damage?
However, it's always up to your Dungeon Master to adjudicate how free actions work. The answers below are some general guidelines, but your DM may choose to rule differently in any of these situations.
1) I hit an enemy with Crane's Wings, which pushes 1. I know I can choose to push 0, but can I Flurry first and then deal damage and push? (as in option B, C, or D above)
Yes you can. The hit has happened, so you can use it then.
2) I hit an enemy with Crane's Wings. Can I push, shift next to them with a move action, and then Flurry? (as in option D above)
No. Free actions on your turn that don't specify otherwise act more or less like reactions. You can use the Flurry after you hit but before damage, and your Dungeon Master may allow you to use it after you've hit and done the damage, but you can't take another action between the hit and the flurry.
3) I use the 5th level Daily power One Hundred Leaves, which is a Close Blast 3 that pushes 2. Is it possible to roll to hit a valid target, then before rolling against other targets, using Centered Flurry of Blows to move another adjacent enemy into the Blast area so that it would also be targeted? (as in C or D but not B)
Unfortunately no to this as well. The targets are determined when the power is originally used. Sliding someone into the burst after the fact would not make a target out of them.
4) I use One Hundred Leaves. Can I use Centered Flurry to slide a MISSED target out of the Blast area before dealing the Miss damage? If so, are they still affected by damage?
Yes, they are still affected by the miss damage. The centered flurry affect doesn't change what happens with the rest of the attack, the targeting or the damage.
