Is there any list of what trophies can be played in basic, standard or global tournaments? So that I know if something is playable for me before I purchase it?
If not, can I exchange it for a different trophy if it is not playable?

All trophies are playables in any room of the game.
Some have conditions that prevent you from playing in basic or standard due to the use of some olds characters but they are very few of them.
You have no limitations regarding the delay or the number of trophies you can have in the same time.
Read carefully the description of the trophy before buying it.

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Collectionneur de cartes