"invokes" is passive and is determined by traits on a check and/or card. There are two wordings around "invokes" and they are very different. Be careful reading which wording is used.
A check invokes a trait if the check has the trait or is a check against a card with the trait.
A bane invokes a trait if it deals damage only of a type that matches the trait. The bane's traits are irrelevant when determining whether or not a bane invokes a trait.
See this post for a detailed description of how to determine what traits a check has. To determine what traits a bane has, check the trait listing on the bane card. To determine if a bane only deals damage of a type, check its powers box for something like "All damage dealt by X is Fire damage" -- if such a line is there, the bane invokes the Fire trait.
When you examine cards, you put them back where they came from in the same order unless the power that let you examine tells you otherwise. In this case, both would go back on top. If you examine multiple cards, examine them one at a time. Resolve the triggers as you examine them. If you would need to shuffle the deck during the course of an examine, finish examining (and putting cards back where you found them) before shuffling.
Read through the Mummy's Mask FAQ, and give the rulebook another perusal as well. This is not a game where you can just look things up as you go along, it has a lot of corner cases and nuances which would be best served by reading the rulebook cover-to-cover once or twice to really understand it all.
"invokes" is passive and is determined by traits on a check and/or card. There are two wordings around "invokes" and they are very different. Be careful reading which wording is used.
A check invokes a trait if the check has the trait or is a check against a card with the trait.
A bane invokes a trait if it deals damage only of a type that matches the trait. The bane's traits are irrelevant when determining whether or not a bane invokes a trait.
Unless I'm misunderstanding something (which is possible) I think that is slightly off, particularly the part about the bane's traits being irrelevant. This is what the MM Rulebook says:
NEW: INVOKES
A check invokes a trait if it has or is against a card that has that trait. A card invokes a trait if it has that trait. A bane also invokes a trait if it deals only damage of the type that matches that trait.
So, if a bane has a trait, then the bane invokes that trait Additionally, if the bane deals only one kind of damage, it invokes that type of damage as a trait.
Also note other cards, not just banes, can technically invoke traits too. So, you could have "boons that invoke the X trait" or "spells that invoke the X trait" as well.
Seconding that Hawkmoon is exactly right, and that the italicized part of skizzerz's post is dead cold wrong.
Alas for the one hour edit limit....
Yep. I was wrong. Whoops!
Technically they stay in the Abyss. Hell is where the devils live, and Abbadon is for daemons :)