Volume 3 of Johnstone's "Sketches of an Elephant"

Volume 3 is still in preparation. Some sections of Part F have been completed; you can try to ask the author for a copy if you're interested. I do not know if much progress has been made on Part E, but here are some alternatives:

• The original reference for the homotopy theory of toposes is [Artin and Mazur, Étale homotopy], and some aspects are discussed in [Moerdijk, Classifying spaces and classifying topoi].
• Model structures on presheaf toposes are the subject of Cisinski's thesis, [Les préfaisceaux comme modèles des types d'homotopie].
• There doesn't seem to be a coherent reference for model structures for sheaves of simplicial sets at this time.
• The original reference for non-abelian cohomology is probably [Giraud, Cohomologie non abélienne].