The statement below is false.
The statement above is correct.
I think power cards should also be eligible, yeah. The power card only talks about "cards", not even "combat cards", but even if it did, I'd say that they still should, because the rules state on page 15:
During combat, the term "Combat cards" also includes Power cards. While Power cards are in a player’s hand or played during a combat round, they are considered Combat cards for the purposes of all rules and special abilities regarding combat.