Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure.
I can play a suppression card on any card 'in play'. I assume that means in play in front of other players' played cards, right?
No, it means *any* of the appropriate cards in play, yours or your opponents'. Suppression is mandatory: for example if you play an animal card with an Insect Suppression icon and you have the only insect in play, it becomes suppressed.