Also assuming it is a lasting effect, even if Daenary is killed before the challenge resolves, if the attacker still wins the challenge the target is stilled killed?
When redirecting with the Crown Regent, I assume that occurs before Daenerys's response ... though I probably would not be able to insist the challenge cannot be redirected if the target has already been chosen
Correct on both counts. Once her Response resolves, it doesn't matter what happens to Dany or her text (blanking, for example). The kill happens if the attacker wins the challenge.
And yes, if the challenge is redirected with Crown Regent, the identity of the defending player changes before her Response is triggered, so she has to choose from among the characters controlled by the new defending player.
Note that if the target has already been chosen, you would be able to insist that the challenge cannot be redirected (by Crown Regent) because the person with the Title missed their chance (assuming it wasn't skipped - eg, "I attack with Dany and choose your Robb Stark for her effect." "Uh, Dude, you jumped the gun. I have to decide whether or not to use Crown Regent before you can trigger her Response."). It's too later for that redirect -- although Varys, Lord Commander and "Supporting" could still make the redirect happen.