Hello, Friend and I were playing a match on TheIronThrone.net. I initiated a power challenge with Alerie Tyrell and he Dracarys'd her. There was an action window provided by the game. As the window appeared, it did not disclose who he Dracarys'd, so I chose my Alerie Tyrell and I returned her to my hand. Turns out he did choose her and I ended up "saving" her from the Dracarys. Was this an invalid play?

Targ player was first player.

First player should get to choose a target first, he definitely dracarys her despite what the game window says so yeah, thats a dead Alerie, Iron bank is an action, not an interrupt so it cannot save from dracarys if the targ player had first action. thats my opinion tho. just think of the game if it were IRL, the program prompt doesn't really matter that much.

Probably the best Lannster card of the cycle?

you cannot use opponent's characters to pay for cost!

Does it possible to cancel this card and ALL of the effects by Hand's Judgement?

The faction card kneel and character returned to hand are a cost and won't be cancelled by a Hand's Judgement. 

What is cancelled is the gold gain and the restriction to play the same titled character again. 

Can you return a character from your discard pile or dead pile with the iron bank will have its due? Or is it only possible to return a character in Play with it?

Nope. Ruling here.

"...Card abilities only interact with, and can only target, cards that are in play, unless the ability text specifically refers to an out of play area or element..."

Discard and dead piles are "Out of play" areas. Check here.