If I attacked with a Rapid Strike Pokemon last turn, then use Ninja Boy to swap it with Zeraora V, would the Zeraora V's "Cross Fist" attack do damage to a Benched Pokemon?
No, all effects carry over, so it would be considered the same Pokemon.
Source: TPCi Rules Team (2021-07-01)
On my last turn, I attacked with Zeraora V's "Cross Fist" attack. If I use a different Zeraora V's "Cross Fist" this turn, will it do extra damage?
Yes, that would work.
Source: Chilling Reign FAQ; TPCi Rules Team (2021-06-17)