When the Ghost in the Dark card is played, do the Money and action of the cancelled card stay spent?
Yes. The Ghost in the Dark card negates the effects of the card, but not its cost in Money, or the action that it requires one of your Senators to use — if applicable. What get negated are all the effects that are listed in the description. So for example, if one Party plays a Sabotage card, they spend their 6 Money and exhaust one Senator. If their target then plays a Ghost in the Dark (paying the 9 Money cost) then the Fleet is not destroyed, but the Money stays spent and the Senator stays exhausted. In particular, if the Assassination card is negated by a Ghost in the Dark, then the Influence spending cannot take place because it is one of the effects of the card. So holding off playing your Ghost in the Dark until after your opponents have spent all their Influence is not a legitimate tactic since the Influence would be refunded.