Does Lord of the Silver Twilight lower the cost to play Cthulhu by 1 for all players or just the controller of LotST? Also, will the story card Nowhere to Hide discard success tokens from conspiracy cards?

Yes for all players.

Conspiracy cards are like story cards so they will lose the success tokens.

Thanks alot. I've noticed you in several of my question threads. You've really been helping out alot. If I can ever return the favor I will. Until then, shield your eyes from the horrors that no man should witness.