I'm sure this has been mentioned a hundred times before, but can wildcards mimic other wildcards? For example, can Spider-Man take on the Calculator team ability, if Assembled was in play and he was next to Len Snart, or vice versa? And would inspiring command on Len Snart work for the wildcards next to him mimicking the calculator team ability?

No, because wildcards copy team abilities not team symbols. Assembled keys off of team symbols, there is no way a non-team member will ever be able to use Assembled. Same goes for Inspiring Command.

Check your feats/BFCs/any other game effects. If it keys off of team ability, wildcards can probably exploit it. If it keys off of team symbol, there's no getting around that; a character must actually have that symbol printed on its dial.

Even though The Society says team ability symbol, only the figures assigned the card need to have the symbol. After that wild cards can copy it

But in that pariticular instance, the Society is completely rewriting the IJL team ability like any other alternate feat. Wildcards aren't copying/using the card, they are copying the TA that one of the friendly characters on the board now posseses. Technically, a wildcard is never using any of the alternate TA cards..