It seems that Asmaria had a dream of Joshua, or so I think. He looked like the picture of Joshua, and she seemed to question if it was the same person she saw in her dream. "Can you hear the wings whispering to you. You understand who I am, right?". I wonder why he felt nostalgic to her. Perhaps the nostalgia and the line "I know someone he reminds me of" is just noting that he reminds her of Rosette since they're siblings.
Poor Rosette, the Magdalene refuses to go after Joshua right now. This makes sense, but it must still be hard for her. Clearly Kate can't risk losing anyone else by marching in unprepared. If she does become Militia that would be for the best. And Remington doing the test behind Kate's back does seem to fit his character, he does dote on her quite a bit. If Asmaria wasn't in danger as well I'm sure him and Chrno could have saved her if she gets in trouble. Still, very reckless to release a demon without letting anyone else know...