Where Does Bluntschli Hide?

Practically, he knows that a dead professional soldier is of no value to anyone; thus, he saves his life by the most expedient method available — he hides in a lady's bedchamber.

What secret of Bluntschli does reveal in Act III?

She admits to leaving a picture of herself for Bluntschli in the pocket of her father's coat that Bluntschli wore when he escaped the house. She assumed he would have seen it there. But Bluntschli did not find the picture, and Raina figures it must still be present in the pocket of the coat that Petkoff is now wearing.

Who realizes Raina is hiding an enemy?

Catherine realizes that he is the man that hid in Raina's room, the same man that she and Raina helped escape. Catherine worries that Sergius and Petkoff, who are conferring over military plans in the library, might encounter the soldier.