Was playing the Avengers TB tonight and a question came up over Hope Summers. When you choose her power does it have to be someone who solo adventured and was on the TB at one point? Also can she choose the Asset ability of someone outside of the game? Like if I don't have Thor on the TB or on my Team but I have him and his card with me can I choose his Asset Ability? This came up as if its choose any that arnt attached that you own some are seeing no reason not to run her. Just curious as I can see it both ways.

Nothing in the description stats that the character must be on the map or formerly attached to the team dial.

Quite simply, if a character could be on the team dial, but isn't (for any reason at all), then she can choose to use its asset ability.

K. Was curious as there is no reason NOT to run Hope on either base since she works that way.

Scarlet Witch's Asset ability isn't useless per se, but in terms of the available Asset abilities so far, usefulness ranks from Hope (best) to Switch (worst).

I remember someone saying somewhere that you had to have the other character's card with you. Is that necessary? If you can e.g. look the card up on your phone, or bring a printout of it with you, would that be good enough?

(I ask because I have Hope but no Spidey, Wolverine, or Switch as I split the Avengers starter with somebody else :/)

Yes, if you want to use the asset ability you must have the card for that asset ability with you.
No, you may not pull it up on your smart phone during the match.
Yes, you may print out the asset ability. Print and Play is perfectly legal. Even if it is printed onto a t-shirt.