I don't think that whole business with General Shaw was about discrediting Harker. It was about disgracing Shaw--thereby rendering him "useless" to the Order--while keeping Grayson's own hands clean. Remember, Harker didn't break that "scoop" himself; he just passed it onto a friend of a friend, so Harker's reputation remains secure. Dracula just tricked Harker into planting a false scandal while maintaining several layers of plausible deniability.
As for Mina: My impression is that Dracula is genuinely conflicted on the subject. He can't stay away from her, but I think part of him is trying to . . . for her sake.
And, yeah, my best guess is that Jayne is trying to "turn" Lucy, to use spy-movie lingo, so she can be used a pawn against Mina . . ..
And vampire-rat will surely return!