I've completed the scene at dragon rock where I've captured Vallarian, but when I bring him back into Hillbrandt I can only imprison and torture him I cannot execute him which I think should move me on in the game. Can anyone help with any part that may have been missed. I'm also not able to exonerate Edward D'arvais

Regarding Vallarian: Have you talked about this with Jeremiah (in front of Hillbrandt's church)? After Vallarian confesses Jeremiah should be willing to start court proceedings with him.

Regarding Edmond d’Arvias: Edmond will be exonerated as soon as Vallarian is burnt. If you haven't arrested him the quest to do so will be cancelled and Edmond will move in front of the Brotherhood’s chapter house. If you have arrested him you can go to Sheriff Contemburry and ask him to let Edmond go after which he moves in front of the chapter house as well.