Your first question slightly puzzles me, as I am not seeing a Mummy's Mask character with exactly that power.
The closest I find is Zadim, who starts with the character power:
You may recharge a card to add your Intelligence skill ( +2) to your check that invokes the Poison ( or Acid or Undead) trait.
I'll assume you are asking about Zadim.
-- He can use this power when he is attempting any check that invokes the indicated trait.
-- He is not playing the card he recharges, so it does not count towards the "only 1 card of each type per check" limit. (The rulebook defines playing a card as either performing an action specified by the card to use a power on the card or choosing to activate a power on a displayed card.)
-- So for combat he can indeed reveal or discard or recharge a weapon and also recharge a card to use this power. In fact, if he revealed the weapon, he could then recharge *that same weapon* to use this power.
Knowing the English meaning of "invoke" wouldn't help you too much, because the game uses the term in a very specific sense. As Hawkmoon says in the linked thread above, the rulebook says a check invokes a trait if:
-- The check has that trait, or
-- The check is against a card that has that trait.
The rulebook also says a check is "against" a card if the card specifies the check (in other words, before-you-act and after-you-act checks listed on a monster's card are checks against the monster's card, just as much as the checks to defeat are).