After perché any kind of clause, with any ordering, can occur, as if they were main clauses. The three sentences in your example are all acceptable as main clause.
Queste faccende sono il mio pane quotidiano is a normally-ordered sentence (a subject with a nominal predicate).
Di me si fida la duchessa has a slightly unusual ordering instead; the standard form would be La duchessa si fida di me (The duchess trusts me). The sentence as given seems to stress that the duchess trusts especially the speaker (so the person he is speaking to should too). And this sentence works the same exact way both as a main clause and as a subordinate clause after perché, while on the other hand “Perché la duchessa si fida di me” would be a perfectly good answer, with a different stress.
So, in principle, any sentence, either standard or with an unusual construction to stress something can also be a perché-sentence, and even a composite period (“Perché dovrei fidarmi di te?” “Perché se non ti fidi, mi rivolgo a qualcun altro”).