Translation:This work always engages him for one hour.
to occupy, to absorb someone or to utilize something, depending on the context. 'in Anspruch nehmen' is somewhat idiomatic. 'ihn' is the someone absorb would also need. I've also found 'make use of smth.' or 'to draw on smth, so' – So, this work always absorbs him for one hour, maybe.
Does it carry a suggestion that he has been commissioned or otherwise obliged to do this work? In English, we might say "This work usually takes him an hour," but perhaps "I engaged him to do the work . . . ."
Oh no, it says nothing about the intention actually. The german sentence only states, that this kind of work takes him one hour each time he does it. Imagine a routinely performed duty that takes exactly one hour each time you do it. That work will always occupy you one hour.
No, that doesn't work in German. It makes no sense. Instead of the idiomatic 'in Anspruch nehmen' you might say: Mit dieser Arbeit ist er immer eine Stunde beschäftigt. - beschäftigt = busy, (pre-)occupied and so on.