America controls an attacking 20/20 creature and Norway is at 20 life.
After Norway declares no blocks, he casts Deflecting Palm, choosing America's creature.

If America has a Deflecting Palm in hand, can they cast it then to re-redirect the damage right then? Do they choose Norway's spell on the stack? If they fail to cast their palm before Norway's resolves, can they cast their palm before damage and choose the redirect effect?

(sorry if this is too straightforward, It came up tonight at fnm and a couple corner-casers wanted clarifications)

America can do it either way. If they cast their Deflecting Palm in response to Norway's Deflecting Palm, that's just fine. If they do it after Norway's Palm resolves, that's just fine too.

When a player is choosing a source of damage, they can choose…well, basically anything they will ever have reason to want to choose. The full list of possible choices is as follows:

• Any permanent currently on the battlefield
  
• Any spell currently on the stack.
  
• Any object referred to by an object on the stack.
  
• Any object referred to by a replacement or prevention effect that's waiting to apply.
  
• Any object referred to by a delayed triggered ability that's waiting to trigger.

The second and fourth ones are the relevant ones here. America can choose Norway's Deflecting Palm as a source and have their own Palm work as it should no matter whether or not Norway's Palm is still on the stack.