When I put Shedinja onto my bench using Ninjask's "Cast-off Shell" Ability, can Eviolite help protect it from damage?
No, because Shedinja is not a "Basic Pokemon"; it is an unevolved Stage-1 Pokemon.
Source: TPCi Rules Team (2012-08-23)
If Eviolite if attached to Zekrom, would its "Bolt Strike" attack do 40 or 20 damage to itself?
Eviolite reduces any damage done to the Basic Pokemon by attacks from either player. So Bolt Strike's self-damage would also be reduced by -20.
Source: Noble Victories FAQ (2011-11-17), PUI Rules Team (2011-11-17)