When I choose someone to select a target for Ticking Mime Bomb, can they target a creature in any nearby game, or must they only select a creature my opponent controls?

They can only target an opponent’s creature in your game.

Hi Mark. Unfinity ruling - when playing Ticking Mime Bomb in Britain can we use our national understanding of the word “pantomime” (musical comedy theatre - see Wikipedia page for pantomime for more details) rather than the separate concept of “mime” the card implies?

The intent of the card is that use mime rather than singing as singing what creature you want them to choose isn’t much of a minigame.