Abilities » Empty Shell
If Garbodor's "Garbotoxin" is present when Shedinja with the "Empty Shell" Ability is KO'd, do you take a prize?
Yes, Empty Shell is turned off by Garbotoxin.
Source: PUI Rules Team (2005-06-23), Dragons Exalted FAQ (2012-08-23) Dragons Exalted FAQ (2012-08-23)
Abilities » Empty Shell | Attacks » Shred
Would Giratina EX's "Shred" attack allow my opponent to knock out my Shednija (with "Empty Shell") and take a prize since the attack says its not affected by any effects on the Defending Pokemon?
The damage done by Shred is not affected by Empty Shell, but that has nothing to do with whether you take a prize or not. You still get no prize because of "Empty Shell".
Source: PUI Rules Team (2006-01-12), Dragons Exalted FAQ (2012-08-23) Dragons Exalted FAQ (2012-08-23)